{"id":24978,"date":"2025-11-24T07:12:11","date_gmt":"2025-11-24T07:12:11","guid":{"rendered":"https:\/\/pokecon.jp\/job\/?p=24978"},"modified":"2025-11-24T07:12:11","modified_gmt":"2025-11-24T07:12:11","slug":"3d%e3%83%a2%e3%83%87%e3%83%ab%e3%82%92%e5%9c%a7%e7%b8%ae%e3%81%99%e3%82%8b%e6%8a%80%e8%a1%932%ef%bc%9arans%e3%81%a8%e3%81%af-reearth-engineering","status":"publish","type":"post","link":"https:\/\/pokecon.jp\/job\/24978\/","title":{"rendered":"3D\u30e2\u30c7\u30eb\u3092\u5727\u7e2e\u3059\u308b\u6280\u88532\uff1arANS\u3068\u306f | Re:Earth Engineering"},"content":{"rendered":"\n<\/p>\n
\n

\u3053\u3093\u306b\u3061\u306f\u3001Eukarya\u306e\u77e2\u6240\u3067\u3059\u3002<\/p>\n

\u4eca\u56de\u306f3D\u30e2\u30c7\u30eb\u5727\u7e2e\u6280\u8853\u306b\u95a2\u3059\u308b\u9023\u8f09\u8a18\u4e8b\u306e\u7b2c2\u56de\u3068\u3057\u3066\u3001rANS<\/strong>\u306b\u3064\u3044\u3066\u53d6\u308a\u4e0a\u3052\u307e\u3059\u3002<\/p>\n

ranged Asymmetric Numerical System<\/strong><\/p>\n

\u3001\u7565\u3057\u3066rANS\u306f\u3001\u30a8\u30f3\u30c8\u30ed\u30d4\u30fc\u7b26\u53f7\u5316<\/em>\u3068\u547c\u3070\u308c\u308b\u6587\u5b57\u306e\u78ba\u7387\u5206\u5e03\u3092\u5229\u7528\u3057\u3066\u6587\u5b57\u5217\u3092\u5727\u7e2e\u3059\u308b\u5727\u7e2e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u4e00\u7a2e\u3067\u3059\u3002<\/p>\n

\u4ed6\u306e\u30a8\u30f3\u30c8\u30ed\u30d4\u30fc\u7b26\u53f7\u5316\u3068\u6bd4\u8f03\u3057\u3066\u3001rANS\u306f\u305d\u306e\u901f\u3055\u3068\u5727\u7e2e\u7387\u306e\u9ad8\u3055\u3067\u77e5\u3089\u308c\u3066\u3044\u307e\u3059\u3002\u5177\u4f53\u7684\u306b\u306f\u3001\u30cf\u30d5\u30de\u30f3\u7b26\u53f7\u5316\u3068\u540c\u7b49\u306e\u901f\u5ea6\u3092\u5b9f\u73fe\u3057\u3064\u3064\u3001\u4e0e\u3048\u3089\u308c\u305f\u78ba\u7387\u5206\u5e03\u306b\u5bfe\u3057\u3066\u6700\u5927\u306e\u5727\u7e2e\u7387\u3092\u9054\u6210\u3067\u304d\u308b\u3053\u3068\u304c\u4fdd\u8a3c\u3055\u308c\u3066\u3044\u307e\u3059\u3002<\/p>\n

rANS\u306f\u30dd\u30fc\u30e9\u30f3\u30c9\u306e\u8a08\u7b97\u6a5f\u79d1\u5b66\u8005J. Duda\u306b\u3088\u3063\u3066\u3001Asymmetric Numerical Systems\uff08ANS\uff09\u3068\u547c\u3070\u308c\u308b\u65b0\u3057\u3044\u30a8\u30f3\u30c8\u30ed\u30d4\u30fc\u7b26\u53f7\u5316\u65cf\u306b\u95a2\u3059\u308b\u4e00\u9023\u306e\u8ad6\u6587\u306e\u4e00\u90e8\u3068\u3057\u30662013\u5e74\u306b\u767a\u8868\u3055\u308c\u307e\u3057\u305f\u3002rANS\u306f\u3001\u305d\u306e\u8a08\u7b97\u52b9\u7387\u306e\u3088\u3055\u3068\u6570\u5b66\u7684\u306b\u4fdd\u8a3c\u3055\u308c\u305f\u6700\u9069\u6027\u304b\u3089\u3001\u307e\u305f\u305f\u304f\u9593\u306b\u4e16\u754c\u3067\u6700\u3082\u5e83\u304f\u4f7f\u7528\u3055\u308c\u308b\u5727\u7e2e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u4e00\u3064\u3068\u306a\u308a\u307e\u3057\u305f\u3002<\/p>\n

\u5b9f\u969b\u306brANS\u304c\u4f7f\u308f\u308c\u3066\u3044\u308b\u4f8b\u3068\u3057\u3066\u306f\u3001\u4f8b\u3048\u3070\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u3082\u306e\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n

    \n
  1. Draco\uff08Google\u306b\u3088\u308b3D\u30e2\u30c7\u30eb\u30b3\u30fc\u30c7\u30c3\u30af\uff09<\/li>\n
  2. JPEG XL\u3001AV1\uff08\u753b\u50cf\/\u52d5\u753b\u30b3\u30fc\u30c7\u30c3\u30af\uff09<\/li>\n
  3. Opus\uff08\u97f3\u58f0\u30b3\u30fc\u30c7\u30c3\u30af\uff09<\/li>\n
  4. Zstd\u304a\u3088\u3073LZFSE\uff08Meta\u304a\u3088\u3073Apple\u306b\u3088\u308b\u6c4e\u7528\u5727\u7e2e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\uff09<\/li>\n<\/ol>\n

    \u307e\u305f\u3001\u3044\u304f\u3064\u304b\u306e\u30aa\u30da\u30ec\u30fc\u30c6\u30a3\u30f3\u30b0\u30b7\u30b9\u30c6\u30e0\u3084\u30d6\u30e9\u30a6\u30b6\u306a\u3069\u306e\u57fa\u76e4\u30b7\u30b9\u30c6\u30e0\u306b\u3082\u7d44\u307f\u8fbc\u307e\u308c\u3066\u3044\u308b\u3053\u3068\u3067\u3082\u77e5\u3089\u308c\u3066\u304a\u308a\u3001\u305d\u306e\u666e\u53ca\u7bc4\u56f2\u306f\u3082\u306f\u3084\u8a08\u308a\u77e5\u308c\u307e\u305b\u3093\u3002\u307e\u3055\u306b\u4eca\u3001\u3053\u306e\u8a18\u4e8b\u3092\u8868\u793a\u3057\u3066\u3044\u308b\u30c7\u30d0\u30a4\u30b9\u4e0a\u3067\u3082rANS\u304c\u52d5\u4f5c\u3057\u3066\u3044\u308b\u304b\u3082\u3057\u308c\u306a\u3044\u30fc\u30fc\u3068\u8a00\u3063\u3066\u3082\u904e\u8a00\u3067\u306f\u306a\u3044\u307b\u3069\u3001\u5b9f\u306frANS\u306f\u3068\u3066\u3082\u8eab\u8fd1\u306a\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306a\u306e\u3067\u3059\u3002<\/p>\n

    rANS\u306f\u300c3D\u30e2\u30c7\u30eb\u5727\u7e2e\u5c02\u7528\u6280\u8853\u300d\u3068\u3044\u3046\u308f\u3051\u3067\u306f\u306a\u304f\u3001\u3088\u308a\u6c4e\u7528\u7684\u306a\u5727\u7e2e\u6280\u8853\u3067\u3059\u304c\u3001\u4eca\u56de3D\u30e2\u30c7\u30eb\u5727\u7e2e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u9023\u8f09\u306b\u3053\u308c\u3092\u542b\u3081\u3066\u3044\u308b\u306e\u306f\u30013D\u5727\u7e2e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u304crANS\u30b3\u30fc\u30c7\u30c3\u30af\u3092\u983b\u7e41\u306b\u6d3b\u7528\u3057\u3066\u3044\u308b\u304b\u3089\u3067\u3059\u3002<\/p>\n

    \u4f8b\u3048\u3070\u3001\u9023\u8f09\u306e\u7b2c1\u56de\u3067\u306f\u3001\u30e1\u30c3\u30b7\u30e5\u306e\u63a5\u7d9a\u6027\u3092\u7279\u6b8a\u306a\u6587\u5b57\u5217\u306b\u5909\u63db\u3059\u308b\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3067\u3042\u308bEdgebreaker\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u898b\u3066\u304d\u307e\u3057\u305f\u3002rANS\u306f\u6587\u5b57\u5217\u3092\u5727\u7e2e\u3067\u304d\u308b\u305f\u3081\u3001\u5f97\u3089\u308c\u305f\u6587\u5b57\u5217\u3092rANS\u30b3\u30fc\u30c0\u30fc\u306b\u5165\u529b\u3059\u308b\u3053\u3068\u3067\u3001\u3088\u308a\u9ad8\u3044\u5727\u7e2e\u7387\u3092\u5b9f\u73fe\u3067\u304d\u307e\u3059\u3002\u3055\u3089\u306b\u3001rANS\u306f\u9802\u70b9\u5ea7\u6a19\u5727\u7e2e\u3084\u30c6\u30af\u30b9\u30c1\u30e3\u5ea7\u6a19\u5727\u7e2e\u306b\u81f3\u308b\u307e\u3067\u3001\u5e45\u5e83\u304f\u6d3b\u7528\u3055\u308c\u3066\u3044\u307e\u3059\u3002<\/p>\n

    \u672c\u8a18\u4e8b\u3067\u306f\u3001rANS\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u57fa\u790e\u3092\u89e3\u8aac\u3057\u3066\u3044\u304d\u307e\u3059\u3002<\/p>\n

    \n

    \ud83d\udca1 Eukarya\u3067\u306f\u3001Google\u306eDraco 3D\u30e2\u30c7\u30eb\u5727\u7e2e\u30e9\u30a4\u30d6\u30e9\u30ea\u3092Rust\u3067\u66f8\u304d\u76f4\u3057\u305fdraco-oxide<\/a>\u3092\u958b\u767a\u3057\u3066\u3044\u307e\u3059\u3002\u3082\u3057\u8208\u5473\u304c\u3042\u308c\u3070\u305c\u3072\u30c1\u30a7\u30c3\u30af\u3057\u3066\u307f\u3066\u304f\u3060\u3055\u3044!<\/p>\n<\/blockquote>\n

    \u8a2d\u5b9a\u3068\u8a18\u6cd5<\/h2>\n

    \u307e\u305a\u3001\u6709\u9650\u306a\u6587\u5b57\u306e\u96c6\u5408S<\/mi><\/mrow>S<\/annotation><\/semantics><\/math><\/span>S<\/span><\/span><\/span><\/span>\u3092\u8003\u3048\u3066\u3001S<\/mi><\/mrow>S<\/annotation><\/semantics><\/math><\/span>S<\/span><\/span><\/span><\/span>\u4e0a\u306b\uff1c\u3067\u793a\u3055\u308c\u308b\u9806\u5e8f\u3092\u56fa\u5b9a\u3057\u307e\u3059\uff08\u4f8b\u3048\u3070\u3001S<\/mi><\/mrow>S<\/annotation><\/semantics><\/math><\/span>S<\/span><\/span><\/span><\/span>\u304c\u82f1\u8a9e\u306e\u5c0f\u6587\u5b57\u30a2\u30eb\u30d5\u30a1\u30d9\u30c3\u30c8\u3067\u3042\u308c\u3070ap<\/mi>:<\/mo>S<\/mi>\u2192<\/mo>[<\/mo>0<\/mn>,<\/mo>1<\/mn>]<\/mo><\/mrow>p: S \\to [0,1]<\/annotation><\/semantics><\/math><\/span>p<\/span>:<\/span><\/span>S<\/span>\u2192<\/span><\/span>[<\/span>0<\/span>,<\/span>1<\/span>]<\/span><\/span><\/span>\u304c\u4e0e\u3048\u3089\u308c\u3066\u3044\u308b\u3068\u3057\u307e\u3057\u3087\u3046\u3002\u78ba\u7387\u5206\u5e03\u3067\u3059\u306e\u3067\u3001\u2211<\/mo>s<\/mi>\u2208<\/mo>S<\/mi><\/mrow><\/msub>p<\/mi>(<\/mo>s<\/mi>)<\/mo>=<\/mo>1<\/mn><\/mrow>\\sum_{s \\in S} p(s)=1<\/annotation><\/semantics><\/math><\/span>\u2211<\/span>s<\/span>\u2208<\/span>S<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>p<\/span>(<\/span>s<\/span>)<\/span>=<\/span><\/span>1<\/span><\/span><\/span><\/span>\u3092\u6e80\u305f\u3057\u307e\u3059\u3002<\/b><\/p>\n

    \u3057\u304b\u3057\u3001rANS\u304c\u52d5\u4f5c\u3059\u308b\u306f\u6574\u6570\u4e0a\u3067\u3059\u306e\u3067\u3001\u56fa\u5b9a\u3055\u308c\u305f\u6b63\u306e\u6574\u6570M<\/mi><\/mrow>M<\/annotation><\/semantics><\/math><\/span>M<\/span><\/span><\/span><\/span><\/p>\n

    \u306b\u5bfe\u3057\u3066\u3001\u96e2\u6563\u78ba\u7387\u5206\u5e03<\/em>\u3068\u547c\u3070\u308c\u308b\u95a2\u6570<\/p>\n

    P<\/mi>:<\/mo>S<\/mi>\u2192<\/mo>N<\/mi><\/mrow>P:S \\to \\N<\/annotation><\/semantics><\/math><\/span>P<\/span>:<\/span><\/span>S<\/span>\u2192<\/span><\/span>N<\/span><\/span><\/span><\/span>\u3092\u6b21\u306e\uff12\u3064\u306e\u6761\u4ef6\u3092\u6e80\u305f\u3059\u3082\u306e\u3068\u3057\u3066\u5b9a\u7fa9\u3057\u307e\u3059\u3002<\/p>\n
      \n
    1. \u2211<\/mo>s<\/mi>\u2208<\/mo>S<\/mi><\/mrow><\/msub>P<\/mi>(<\/mo>s<\/mi>)<\/mo>=<\/mo>M<\/mi><\/mrow>\\sum_{s \\in S} P(s) = M<\/annotation><\/semantics><\/math><\/span>\u2211<\/span>s<\/span>\u2208<\/span>S<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>P<\/span>(<\/span>s<\/span>)<\/span>=<\/span><\/span>M<\/span><\/span><\/span><\/span>\u3002<\/li>\n
    2. \u5404s<\/mi>\u2208<\/mo>S<\/mi><\/mrow>s \\in S<\/annotation><\/semantics><\/math><\/span>s<\/span>\u2208<\/span><\/span>S<\/span><\/span><\/span><\/span>\u306b\u3064\u3044\u3066P<\/mi>(<\/mo>s<\/mi>)<\/mo>\u223c<\/mo>p<\/mi>(<\/mo>s<\/mi>)<\/mo>M<\/mi><\/mrow>P(s) \\sim p(s)M<\/annotation><\/semantics><\/math><\/span>P<\/span>(<\/span>s<\/span>)<\/span>\u223c<\/span><\/span>p<\/span>(<\/span>s<\/span>)<\/span>M<\/span><\/span><\/span><\/span>\u3002<\/li>\n<\/ol>\n

      \u3055\u3089\u306b\u3001C<\/mi>(<\/mo>s<\/mi>)<\/mo>=<\/mo>\u2211<\/mo>t<\/mi>\u2208<\/mo>S<\/mi>:<\/mo>t<\/mi>s<\/mi><\/mo><\/mrow><\/msub>P<\/mi>(<\/mo>t<\/mi>)<\/mo><\/mrow>C(s) = \\sum_{t\\in S:t <\/annotation><\/semantics><\/math><\/span>C<\/span>(<\/span>s<\/span>)<\/span>=<\/span><\/span>\u2211<\/span>t<\/span>\u2208<\/span>S<\/span>:<\/span>t<\/span>s<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>P<\/span>(<\/span>t<\/span>)<\/span><\/span><\/span><\/span>\u3068\u5b9a\u7fa9\u3057\u307e\u3059\u3002C<\/mi>(<\/mo>s<\/mi>)<\/mo><\/mrow>C(s)<\/annotation><\/semantics><\/math><\/span>C<\/span>(<\/span>s<\/span>)<\/span><\/span><\/span><\/span>\u3092s<\/mi><\/mrow>s<\/annotation><\/semantics><\/math><\/span>s<\/span><\/span><\/span><\/span>\u306e\u7bc4\u56f2<\/strong>\u3078\u306e\u30aa\u30d5\u30bb\u30c3\u30c8<\/strong>\u3068\u547c\u3076\u3053\u3068\u306b\u3057\u307e\u3057\u3087\u3046\u3002\u3053\u308c\u3089\u306e\u8a2d\u5b9a\u306f\u30010<\/mn><\/mrow>0<\/annotation><\/semantics><\/math><\/span>0<\/span><\/span><\/span><\/span>\u304b\u3089M<\/mi>\u2212<\/mo>1<\/mn><\/mrow>M-1<\/annotation><\/semantics><\/math><\/span>M<\/span>\u2212<\/span><\/span>1<\/span><\/span><\/span><\/span>\u307e\u3067\u306e\u6574\u6570\u3092\u2223<\/mi>S<\/mi>\u2223<\/mi><\/mrow>|S|<\/annotation><\/semantics><\/math><\/span>\u2223<\/span>S<\/span>\u2223<\/span><\/span><\/span><\/span>\u500b\u306e\u7bc4\u56f2<\/strong>\u3078\u3068\u5206\u3051\u308b\u3068\u3044\u3046\u76ee\u7684\u304c\u3042\u308a\u307e\u3059\u3002<\/span><\/p>\n

      \u30a4\u30e1\u30fc\u30b8\u3067\u7406\u89e3\u3057\u305f\u3044\u65b9\u306b\u306f\u3001\u56f3\uff11\u304c\u53c2\u8003\u306b\u306a\u308b\u3068\u601d\u3044\u307e\u3059\u3002<\/p>\n

      \"\u56f31:
      \u56f31: \u8a2d\u5b9a\u306e\u4f8b\u3002S={a,b,c,d} \uff08\u3053\u306e\u9806\u756a\uff09\u306e\u30a2\u30eb\u30d5\u30a1\u30d9\u30c3\u30c8\u306b\u5bfe\u3057\u3066P (b)=3\u3001\u2026\u3068\u3044\u3063\u305f\u69d8\u5b50\u3067\u96e2\u6563\u78ba\u7387\u5206\u5e03\u304c\u5b9a\u3081\u3089\u308c\u3066\u3044\u308b\u3002\u3064\u307e\u308a\u3001\u4f8b\u3048\u3070\u6587\u5b57\u5217\u4e2d\u306e\u3068\u3042\u308b\u4f4d\u7f6e\u306ba\u304c\u73fe\u308c\u308b\u78ba\u7387\u306fP(a) \/ M * 100 = 40%\u3068\u5b9a\u7fa9\u3055\u308c\u3066\u3044\u308b\u3002\u30aa\u30d5\u30bb\u30c3\u30c8\u3068\u7bc4\u56f2\u3082\u793a\u3055\u308c\u3066\u3044\u308b\u3002\u3053\u308c\u3088\u308a\u3001 a\u306e\u7bc4\u56f2\u306f0\u304b\u30894\u307e\u3067, b\u306e\u7bc4\u56f2\u306f4\u304b\u30897\u307e\u3067\u3068\u3044\u3063\u305f\u3075\u3046\u306b\u5b9a\u7fa9\u3055\u308c\u3066\u3044\u308b\u3002<\/figcaption><\/figure>\n

      \u5727\u7e2e<\/h2>\n

      \u305d\u308c\u3067\u306f\u3001\u5b9f\u969b\u306b\u5727\u7e2e\u306e\u65b9\u6cd5\u306b\u3064\u3044\u3066\u898b\u3066\u3044\u304d\u307e\u3059\u3002S<\/mi><\/mrow>S<\/annotation><\/semantics><\/math><\/span>S<\/span><\/span><\/span><\/span>\u4e2d\u306e\u6587\u5b57\u3067\u3067\u304d\u305f\u6587\u5b57\u5217(<\/mo>s<\/mi>1<\/mn><\/msub>,<\/mo>s<\/mi>2<\/mn><\/msub>,<\/mo>\u22ef<\/mo>\u2009<\/mtext>,<\/mo>s<\/mi>m<\/mi><\/msub>)<\/mo><\/mrow>(s_1, s_2, \\cdots, s_m)<\/annotation><\/semantics><\/math><\/span>(<\/span>s<\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span>s<\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span>\u22ef<\/span>,<\/span>s<\/span>m<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span>\uff08m<\/mi><\/mrow>m<\/annotation><\/semantics><\/math><\/span>m<\/span><\/span><\/span><\/span>\u306f\u6574\u6570\uff09\u3092\u7b26\u53f7\u5316\u3057\u305f\u3044\u3068\u3057\u307e\u3057\u3087\u3046\u3002\u307e\u305a\u3001\u521d\u671f\u72b6\u614b<\/strong>\u3092X<\/mi>0<\/mn><\/msub>=<\/mo>0<\/mn><\/mrow>X_0=0<\/annotation><\/semantics><\/math><\/span>X<\/span>0<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span>0<\/span><\/span><\/span><\/span>\u3068\u7f6e\u304d\u307e\u3059\u3002rANS\u306f\u3053\u306e\u72b6\u614b\u3092\u518d\u5e30\u7684\u306b\u66f4\u65b0\u3059\u308b\u3053\u3068\u3067X<\/mi>1<\/mn><\/msub>,<\/mo>X<\/mi>2<\/mn><\/msub>,<\/mo>\u22ef<\/mo><\/mrow>X_1, X_2, \\cdots<\/annotation><\/semantics><\/math><\/span>X<\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span>X<\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span>\u22ef<\/span><\/span><\/span><\/span>\u3068\u9806\u306b\u8a08\u7b97\u3057\u3066\u3044\u304d\u3001\u6700\u7d42\u7684\u306bX<\/mi>m<\/mi><\/msub><\/mrow>X_m<\/annotation><\/semantics><\/math><\/span>X<\/span>m<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3092\u8a08\u7b97\u3057\u307e\u3059\u3002\u305d\u306eX<\/mi>m<\/mi><\/msub><\/mrow>X_m<\/annotation><\/semantics><\/math><\/span>X<\/span>m<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3053\u305d\u304crANS\u306e\u51fa\u529b\u3001\u3064\u307e\u308a\u5727\u7e2e\u30c7\u30fc\u30bf\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n

      \u5404\u518d\u5e30\u30b9\u30c6\u30c3\u30d7\u306e\u52d5\u4f5c\u306f\u6b21\u306e\u901a\u308a\u3067\u3059\u3002\u7b26\u53f7\u5316\u30b9\u30c6\u30c3\u30d7\u3092\u8868\u3059\u95a2\u6570\u3092E<\/mi>:<\/mo>Z<\/mi>\u00d7<\/mo>S<\/mi>\u2192<\/mo>Z<\/mi><\/mrow>E:\\Z\\times S \\to \\Z<\/annotation><\/semantics><\/math><\/span>E<\/span>:<\/span><\/span>Z<\/span>\u00d7<\/span><\/span>S<\/span>\u2192<\/span><\/span>Z<\/span><\/span><\/span><\/span>\u3068\u3059\u308b\u3068\u3001\u7b26\u53f7\u5316\u30b9\u30c6\u30c3\u30d7\u306f\u5404\u6642\u523bi<\/mi>\u2208<\/mo>{<\/mo>1<\/mn>,<\/mo>\u22ef<\/mo>\u2009<\/mtext>,<\/mo>m<\/mi>}<\/mo><\/mrow>i \\in \\{1,\\cdots, m\\}<\/annotation><\/semantics><\/math><\/span>i<\/span>\u2208<\/span><\/span>{<\/span>1<\/span>,<\/span>\u22ef<\/span>,<\/span>m<\/span>}<\/span><\/span><\/span><\/span>\u306b\u3064\u3044\u3066X<\/mi>i<\/mi><\/msub>=<\/mo>E<\/mi>(<\/mo>X<\/mi>i<\/mi>\u2212<\/mo>1<\/mn><\/mrow><\/msub>,<\/mo>s<\/mi>i<\/mi><\/msub>)<\/mo><\/mrow>X_i = E(X_{i-1},s_i)<\/annotation><\/semantics><\/math><\/span>X<\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span>E<\/span>(<\/span>X<\/span>i<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span>s<\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span>\u3068\u66f8\u304f\u3053\u3068\u304c\u3067\u304d\u307e\u3059\uff08\u3053\u306e\u8a18\u4e8b\u306e\u4e2d\u3067\u306f\u3001s<\/mi>\u2208<\/mo>S<\/mi><\/mrow>s\\in S<\/annotation><\/semantics><\/math><\/span>s<\/span>\u2208<\/span><\/span>S<\/span><\/span><\/span><\/span>\u304c\u56fa\u5b9a\u3055\u308c\u3066\u3044\u308b\u5834\u5408\u3001\u4fbf\u5b9c\u4e0aX<\/mi>i<\/mi><\/msub>=<\/mo>E<\/mi>s<\/mi><\/msub>(<\/mo>X<\/mi>i<\/mi>\u2212<\/mo>1<\/mn><\/mrow><\/msub>)<\/mo><\/mrow>X_i = E_s(X_{i-1})<\/annotation><\/semantics><\/math><\/span>X<\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span>E<\/span>s<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>X<\/span>i<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span>\u3068\u66f8\u304f\u3053\u3068\u3082\u3042\u308a\u307e\u3059\uff09\u3002<\/p>\n

      \u307e\u305a\u3001X<\/mi>i<\/mi>\u2212<\/mo>1<\/mn><\/mrow><\/msub><\/mrow>X_{i-1}<\/annotation><\/semantics><\/math><\/span>X<\/span>i<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3092P<\/mi>(<\/mo>s<\/mi>i<\/mi><\/msub>)<\/mo><\/mrow>P(s_i)<\/annotation><\/semantics><\/math><\/span>P<\/span>(<\/span>s<\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span>\u3067\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u9664\u7b97\u3057\u305f\u5546q<\/mi><\/mrow>q<\/annotation><\/semantics><\/math><\/span>q<\/span><\/span><\/span><\/span>\u3068\u4f59\u308ar<\/mi><\/mrow>r<\/annotation><\/semantics><\/math><\/span>r<\/span><\/span><\/span><\/span>\u3092\u8a08\u7b97\u3057\u307e\u3059\u3002\u3064\u307e\u308a\u3001\u6b21\u3092\u6e80\u305f\u3059\u6b63\u306e\u6574\u6570q<\/mi><\/mrow>q<\/annotation><\/semantics><\/math><\/span>q<\/span><\/span><\/span><\/span>\u3068r<\/mi>P<\/mi>(<\/mo>s<\/mi>i<\/mi><\/msub>)<\/mo><\/mo><\/mrow>r<\/annotation><\/semantics><\/math><\/span>r<\/span><\/span>P<\/span>(<\/span>s<\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span>\u3092\u6c42\u3081\u307e\u3059\u3002<\/span><\/p>\n

      X<\/mi>i<\/mi>\u2212<\/mo>1<\/mn><\/mrow><\/msub>=<\/mo>P<\/mi>(<\/mo>s<\/mi>i<\/mi><\/msub>)<\/mo>q<\/mi>+<\/mo>r<\/mi>.<\/mi><\/mrow><\/mstyle><\/mtd><\/mtr><\/mtable>\\begin{align}\nX_{i-1} = P(s_i) q + r.\n\\end{align}<\/annotation><\/semantics><\/math><\/span>X<\/span>i<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span>P<\/span>(<\/span>s<\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span>q<\/span>+<\/span>r<\/span>.<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

      \u6b21\u306bX<\/mi>i<\/mi><\/msub><\/mrow>X_i<\/annotation><\/semantics><\/math><\/span>X<\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3092\u4ee5\u4e0b\u306e\u5f0f\u3067\u8a08\u7b97\u3057\u307e\u3059\u3002<\/p>\n

      X<\/mi>i<\/mi><\/msub>=<\/mo>E<\/mi>(<\/mo>X<\/mi>i<\/mi>\u2212<\/mo>1<\/mn><\/mrow><\/msub>,<\/mo>s<\/mi>)<\/mo>=<\/mo>q<\/mi>M<\/mi>+<\/mo>C<\/mi>(<\/mo>s<\/mi>i<\/mi><\/msub>)<\/mo>+<\/mo>r<\/mi><\/mrow><\/mstyle><\/mtd><\/mtr><\/mtable>\\begin{align}\nX_i = E(X_{i-1},s) = q M + C(s_i) + r\n\\end{align}<\/annotation><\/semantics><\/math><\/span>X<\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span>E<\/span>(<\/span>X<\/span>i<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span>s<\/span>)<\/span>=<\/span>qM<\/span>+<\/span>C<\/span>(<\/span>s<\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span>+<\/span>r<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

      \u5727\u7e2e\u306e\u30b9\u30c6\u30c3\u30d7\u306f\u4ee5\u4e0a\u3067\u3059\u3002\u3068\u3066\u3082\u5358\u7d14\u3067\u3059\u304c\u3001\u4f55\u304c\u8d77\u3053\u3063\u3066\u3044\u308b\u304b\u306f\u308f\u304b\u308a\u306b\u304f\u3044\u306e\u3067\u3001\u5c11\u3057\u89e3\u8aac\u3092\u3057\u307e\u3059\u3002<\/p>\n

      \u5024q<\/mi><\/mrow>q<\/annotation><\/semantics><\/math><\/span>q<\/span><\/span><\/span><\/span>\u306f\u524d\u306e\u72b6\u614bX<\/mi>i<\/mi>\u2212<\/mo>1<\/mn><\/mrow><\/msub><\/mrow>X_{i-1}<\/annotation><\/semantics><\/math><\/span>X<\/span>i<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u306e\u5727\u7e2e\u7248\u3092\u8868\u3057\u3066\u3044\u307e\u3059\u3002q<\/mi><\/mrow>q<\/annotation><\/semantics><\/math><\/span>q<\/span><\/span><\/span><\/span>\u306bM<\/mi><\/mrow>M<\/annotation><\/semantics><\/math><\/span>M<\/span><\/span><\/span><\/span>\u3092\u304b\u3051\u3066\u3044\u308b\u306e\u306f\u3001\u305d\u306e\u5f8c\u306b\u8db3\u3055\u308c\u308b\u6570\u306e\u305f\u3081\u306b\u30b9\u30da\u30fc\u30b9\u3092\u4f5c\u308b\u305f\u3081\u3067\u3059\u3002<\/p>\n

      \u3053\u306e\u3053\u3068\u306f\u6574\u6570\u3092M<\/mi><\/mrow>M<\/annotation><\/semantics><\/math><\/span>M<\/span><\/span><\/span><\/span>\u9032\u6cd5\u3067\u8868\u73fe\u3059\u308b\u3068\u308f\u304b\u308a\u3084\u3059\u3044\u3067\u3059\u3002M<\/mi><\/mrow>M<\/annotation><\/semantics><\/math><\/span>M<\/span><\/span><\/span><\/span>\u9032\u6cd5\u306e\u6570\u306bM<\/mi><\/mrow>M<\/annotation><\/semantics><\/math><\/span>M<\/span><\/span><\/span><\/span>\u3092\u639b\u3051\u308b\u3068\u5404\u6841\u304c1\u3064\u305a\u3064\u5de6\u306b\u305a\u308c\u3066\u3001\u6700\u4e0b\u4f4d\u306e\u4f4d\u7f6e\u306b0\u304c\u633f\u5165\u3055\u308c\u308b\u306e\u304c\u308f\u304b\u308b\u3068\u601d\u3044\u307e\u3059\u304c\u3001\u3053\u3046\u3057\u3066\u3067\u304d\u305f\u6570\u306b\u96c6\u5408{<\/mo>0<\/mn>,<\/mo>\u2026<\/mo>,<\/mo>M<\/mi>\u2212<\/mo>1<\/mn>}<\/mo><\/mrow>\\{0,\u2026,M\u22121\\}<\/annotation><\/semantics><\/math><\/span>{<\/span>0<\/span>,<\/span>\u2026<\/span>,<\/span>M<\/span>\u2212<\/span><\/span>1<\/span>}<\/span><\/span><\/span><\/span>\u306e\u4e2d\u304b\u3089\u3072\u3068\u3064\u6570\u3092\u9078\u3093\u3067\u8db3\u3057\u305f\u3068\u3053\u308d\u3067\u3001\uff12\u6841\u76ee\u4ee5\u4e0a\u306e\u6570\u306f\u5909\u308f\u308a\u307e\u305b\u3093\u3002\u6700\u5f8c\u306b\u8db3\u3055\u308c\u3066\u3044\u308bC<\/mi>(<\/mo>s<\/mi>i<\/mi><\/msub>)<\/mo>+<\/mo>r<\/mi><\/mrow>C(s_i) + r<\/annotation><\/semantics><\/math><\/span>C<\/span>(<\/span>s<\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span>+<\/span><\/span>r<\/span><\/span><\/span><\/span>\u306f0\u4ee5\u4e0aM<\/mi>\u2212<\/mo>1<\/mn><\/mrow>M-1<\/annotation><\/semantics><\/math><\/span>M<\/span>\u2212<\/span><\/span>1<\/span><\/span><\/span><\/span>\u4ee5\u4e0b\u306a\u306e\u3067\u3001\u3053\u306e\u6761\u4ef6\u3092\u6e80\u305f\u3057\u3066\u3044\u308b\u3068\u3044\u3046\u308f\u3051\u3067\u3059\u3002<\/p>\n

      \u3055\u3066\u3001\u6b21\u306eC<\/mi>(<\/mo>s<\/mi>i<\/mi><\/msub>)<\/mo><\/mrow>C(s_i)<\/annotation><\/semantics><\/math><\/span>C<\/span>(<\/span>s<\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span>\u3067\u3059\u304c\u3001\u3053\u308c\u306f\u3069\u306e\u7bc4\u56f2\u3092\u4f7f\u3063\u3066\u3044\u308b\u306e\u304b\u3092\u899a\u3048\u3066\u304a\u304f\u305f\u3081\u306b\u8a18\u9332\u3055\u308c\u3066\u3044\u307e\u3059\u3002\u3069\u306e\u7bc4\u56f2\u3092\u4f7f\u3063\u3066\u3044\u308b\u304b\u304c\u308f\u304b\u308c\u3070\u3001\u3069\u306e\u6587\u5b57\u304c\u7b26\u53f7\u5316\u3055\u308c\u305f\u304b\u3082\u5f8c\u3067\u601d\u3044\u51fa\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u306d\u3002r<\/mi><\/mrow>r<\/annotation><\/semantics><\/math><\/span>r<\/span><\/span><\/span><\/span>\u306f(1)\u306e\u5f0f\u3067\u4f7f\u308f\u308c\u3066\u3044\u308b\u901a\u308a\u3001\u89e3\u51cd\u6642\u306bq<\/mi><\/mrow>q<\/annotation><\/semantics><\/math><\/span>q<\/span><\/span><\/span><\/span>\u304b\u3089X<\/mi>i<\/mi>\u2212<\/mo>1<\/mn><\/mrow><\/msub><\/mrow>X_{i-1}<\/annotation><\/semantics><\/math><\/span>X<\/span>i<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3092\u5fa9\u5143\u3059\u308b\u305f\u3081\u306b\u6b20\u304b\u305b\u306a\u3044\u60c5\u5831\u3067\u3059\u306e\u3067\u3001\u8a18\u9332\u3055\u308c\u3066\u3044\u307e\u3059\u3002<\/p>\n

      \u89e3\u51cd<\/h2>\n

      \u3055\u3066\u3001\u5727\u7e2e\u306b\u3088\u3063\u3066\u6587\u5b57\u5217\u304b\u3089\uff11\u3064\u306e\u5de8\u5927\u306a\u6574\u6570X<\/mi>m<\/mi><\/msub><\/mrow>X_m<\/annotation><\/semantics><\/math><\/span>X<\/span>m<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3092\u4f5c\u308b\u3053\u3068\u306b\u6210\u529f\u3057\u307e\u3057\u305f\u3002\u3057\u304b\u3057\u3001\u3053\u306e\u5de8\u5927\u306a\u6574\u6570\u304b\u3089\u4e00\u4f53\u3069\u306e\u3088\u3046\u306b\u3057\u3066\u6587\u5b57\u5217\u3092\u89e3\u51cd\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u306e\u3067\u3057\u3087\u3046\u304b\uff1f\u3053\u306e\u7bc0\u3067\u306f\u89e3\u51cd\u306e\u65b9\u6cd5\u3092\u898b\u3066\u3044\u304d\u307e\u3059\u3002<\/p>\n

      rANS\u3067\u7b26\u53f7\u5316\u3055\u308c\u305f\u30c7\u30fc\u30bf\u306e\u5fa9\u53f7\u5316\u306f\u3001\u7b26\u53f7\u5316\u30d7\u30ed\u30bb\u30b9\u3092\u9006\u306b\u305f\u3069\u3063\u3066\u3044\u304f\u3053\u3068\u306b\u3088\u3063\u3066\u5b9f\u73fe\u3057\u307e\u3059\u3002\u3053\u308c\u306f\u3064\u307e\u308a\u3001\u6700\u5f8c\u306b\u7b26\u53f7\u5316\u3055\u308c\u305f\u6587\u5b57\u304c\u6700\u521d\u306b\u5fa9\u53f7\u5316\u3055\u308c\u308b\u3068\u3044\u3046\u3053\u3068\u3067\u3059\u3002<\/p>\n

      \u3055\u3089\u306b\u5177\u4f53\u7684\u306b\u8a00\u3048\u3070\u3001i<\/mi><\/mrow>i<\/annotation><\/semantics><\/math><\/span>i<\/span><\/span><\/span><\/span>\u500b\u306e\u6587\u5b57\u3092\u7b26\u53f7\u5316\u3057\u305f\u5f8c\u306e\u72b6\u614b\u5024X<\/mi>i<\/mi><\/msub><\/mrow>X_i<\/annotation><\/semantics><\/math><\/span>X<\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u304c\u4e0e\u3048\u3089\u308c\u3066\u3044\u308b\u3068\u304d\u3001\u307e\u305as<\/mi>i<\/mi><\/msub><\/mrow>s_i<\/annotation><\/semantics><\/math><\/span>s<\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3092\u5fa9\u5143\u3057\u3001\u6b21\u306bX<\/mi>i<\/mi>\u2212<\/mo>1<\/mn><\/mrow><\/msub><\/mrow>X_{i-1}<\/annotation><\/semantics><\/math><\/span>X<\/span>i<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3092\u8a08\u7b97\u3059\u308b\u3001\u3068\u3044\u3046\u306e\u304c\u5404\u5fa9\u53f7\u5316\u30b9\u30c6\u30c3\u30d7\u306e\u6982\u8981\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n

      \u3053\u3053\u3067\u3082\u5fc5\u8981\u306a\u8a18\u6cd5\u3092\u5c0e\u5165\u3057\u307e\u3059\u3002\u7b26\u53f7\u5316\u306e\u5834\u5408\u3068\u540c\u69d8\u306b\u3001\u5fa9\u53f7\u5316\u95a2\u6570\u3092D<\/mi>:<\/mo>Z<\/mi>\u2192<\/mo>Z<\/mi>\u00d7<\/mo>S<\/mi><\/mrow>D:\\Z\\to\\Z\\times S<\/annotation><\/semantics><\/math><\/span>D<\/span>:<\/span><\/span>Z<\/span>\u2192<\/span><\/span>Z<\/span>\u00d7<\/span><\/span>S<\/span><\/span><\/span><\/span>\u3067\u8868\u3057\u307e\u3059\u3002\u3059\u306a\u308f\u3061\u3001\u5404\u6642\u523bi<\/mi>\u2208<\/mo>{<\/mo>1<\/mn>,<\/mo>\u22ef<\/mo>\u2009<\/mtext>,<\/mo>m<\/mi>}<\/mo><\/mrow>i\\in\\{1,\\cdots,m\\}<\/annotation><\/semantics><\/math><\/span>i<\/span>\u2208<\/span><\/span>{<\/span>1<\/span>,<\/span>\u22ef<\/span>,<\/span>m<\/span>}<\/span><\/span><\/span><\/span>\u306b\u3064\u3044\u3066D<\/mi>(<\/mo>X<\/mi>i<\/mi><\/msub>)<\/mo>=<\/mo>(<\/mo>X<\/mi>i<\/mi>\u2212<\/mo>1<\/mn><\/mrow><\/msub>,<\/mo>s<\/mi>i<\/mi><\/msub>)<\/mo><\/mrow>D(X_i) = (X_{i-1},s_i)<\/annotation><\/semantics><\/math><\/span>D<\/span>(<\/span>X<\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span>=<\/span><\/span>(<\/span>X<\/span>i<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span>s<\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span>\u3068\u66f8\u304f\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n

      \u307e\u305aX<\/mi>i<\/mi><\/msub><\/mrow>X_i<\/annotation><\/semantics><\/math><\/span>X<\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3092M<\/mi><\/mrow>M<\/annotation><\/semantics><\/math><\/span>M<\/span><\/span><\/span><\/span>\u3067\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u9664\u7b97\u3092\u884c\u3044\u307e\u3059\u3002\u3064\u307e\u308a\u3001\u6b21\u3092\u6e80\u305f\u3059\u6b63\u306e\u6574\u6570Q<\/mi><\/mrow>Q<\/annotation><\/semantics><\/math><\/span>Q<\/span><\/span><\/span><\/span>\u3068R<\/mi>M<\/mi><\/mo><\/mrow>R<\/annotation><\/semantics><\/math><\/span>R<\/span><\/span>M<\/span><\/span><\/span><\/span>\u3092\u8a08\u7b97\u3059\u3057\u307e\u3059\u3002<\/span><\/p>\n

      X<\/mi>i<\/mi><\/msub>=<\/mo>M<\/mi>Q<\/mi>+<\/mo>R<\/mi><\/mrow>X_i = M Q + R<\/annotation><\/semantics><\/math><\/span>X<\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span>MQ<\/span>+<\/span><\/span>R<\/span><\/span><\/span><\/span><\/span><\/p>\n

      R<\/mi><\/mrow>R<\/annotation><\/semantics><\/math><\/span>R<\/span><\/span><\/span><\/span>\u306fM<\/mi><\/mrow>M<\/annotation><\/semantics><\/math><\/span>M<\/span><\/span><\/span><\/span>\u3088\u308a\u5c0f\u3055\u3044\u6b63\u306e\u6574\u6570\u3067\u3042\u308b\u305f\u3081\u3001R<\/mi><\/mrow>R<\/annotation><\/semantics><\/math><\/span>R<\/span><\/span><\/span><\/span>\u3092\u542b\u3080\u7bc4\u56f2\u3092\u6301\u3064\u6587\u5b57s<\/mi>i<\/mi><\/msub>\u2208<\/mo>S<\/mi><\/mrow>s_i\\in S<\/annotation><\/semantics><\/math><\/span>s<\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2208<\/span><\/span>S<\/span><\/span><\/span><\/span>\u304c\u5b58\u5728\u3059\u308b\u3053\u3068\u304c\u3044\u3048\u307e\u3059\u3002\u3059\u306a\u308f\u3061\u3001<\/p>\n

      s<\/mi>i<\/mi><\/msub>=<\/mo>max<\/mi>\u2061<\/mo>{<\/mo>s<\/mi>:<\/mo>C<\/mi>(<\/mo>s<\/mi>)<\/mo>\u2264<\/mo>R<\/mi>}<\/mo><\/mrow><\/mrow>s_{i} = \\max \\left\\{s : C(s) \\leq R \\right \\}<\/annotation><\/semantics><\/math><\/span>s<\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span>max<\/span>{<\/span>s<\/span>:<\/span>C<\/span>(<\/span>s<\/span>)<\/span>\u2264<\/span>R<\/span>}<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

      \u3068\u3044\u3046\u8a08\u7b97\u3092\u3059\u308b\u3053\u3068\u3067s<\/mi>i<\/mi><\/msub><\/mrow>s_i<\/annotation><\/semantics><\/math><\/span>s<\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3092\u5fa9\u5143\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n

      \u3061\u306a\u307f\u306b\u3053\u306e\u8a08\u7b97\u306f\u3001{<\/mo>0<\/mn>,<\/mo>1<\/mn>,<\/mo>\u22ef<\/mo>\u2009<\/mtext>,<\/mo>M<\/mi>\u2212<\/mo>1<\/mn>}<\/mo><\/mrow>\\{0,1,\\cdots,M-1\\}<\/annotation><\/semantics><\/math><\/span>{<\/span>0<\/span>,<\/span>1<\/span>,<\/span>\u22ef<\/span>,<\/span>M<\/span>\u2212<\/span><\/span>1<\/span>}<\/span><\/span><\/span><\/span>\u306e\u5404\u5024\u3068\u305d\u308c\u3092\u542b\u3080\u7bc4\u56f2\u3092\u6301\u3064\u6587\u5b57\u306e\u8868\u3092\u5148\u306b\u8a08\u7b97\u3057\u3066\u304a\u304f\u3053\u3068\u3067\u52b9\u7387\u7684\u306b\u5b9f\u88c5\u3067\u304d\u307e\u3059\u3002<\/p>\n

      s<\/mi>i<\/mi><\/msub><\/mrow>s_i<\/annotation><\/semantics><\/math><\/span>s<\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u304c\u7279\u5b9a\u3067\u304d\u305f\u3089\u3001\u6b8b\u308a\u306fX<\/mi>i<\/mi>\u2212<\/mo>1<\/mn><\/mrow><\/msub><\/mrow>X_{i-1}<\/annotation><\/semantics><\/math><\/span>X<\/span>i<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3092\u8a08\u7b97\u3059\u308b\u306e\u307f\u3067\u3059\u3002\u307e\u305a\u3001\u6b21\u306e\u7b49\u5f0f\u304c\u6210\u308a\u7acb\u3064\u3053\u3068\u304c\u89e3\u308b\u3068\u601d\u3044\u307e\u3059\u3002<\/p>\n

      R<\/mi><\/mstyle><\/mtd>=<\/mo>C<\/mi>(<\/mo>s<\/mi>i<\/mi><\/msub>)<\/mo>+<\/mo>r<\/mi><\/mrow><\/mstyle><\/mtd><\/mtr>Q<\/mi><\/mstyle><\/mtd>=<\/mo>q<\/mi><\/mrow><\/mstyle><\/mtd><\/mtr><\/mtable>\\begin{align}\nR &= C(s_i)+r \\\\\nQ &= q\n\\end{align}<\/annotation><\/semantics><\/math><\/span>R<\/span><\/span><\/span>Q<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span>=<\/span>C<\/span>(<\/span>s<\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span>+<\/span>r<\/span><\/span><\/span>=<\/span>q<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

      \u3053\u3053\u3067q<\/mi><\/mrow>q<\/annotation><\/semantics><\/math><\/span>q<\/span><\/span><\/span><\/span>\u3068r<\/mi><\/mrow>r<\/annotation><\/semantics><\/math><\/span>r<\/span><\/span><\/span><\/span>\u306f\u524d\u306e\u7bc0\u306e\u7b26\u53f7\u5316\u95a2\u6570E<\/mi><\/mrow>E<\/annotation><\/semantics><\/math><\/span>E<\/span><\/span><\/span><\/span>\u3067\u5b9a\u7fa9\u3055\u308c\u305f\u5024\u3067\u3059\u3002\u7b49\u5f0f(3)\u3068(4)\u3092\u4f7f\u3063\u3066\u7b49\u5f0f(1)\u306e\u5909\u6570q<\/mi><\/mrow>q<\/annotation><\/semantics><\/math><\/span>q<\/span><\/span><\/span><\/span>\u3068r<\/mi><\/mrow>r<\/annotation><\/semantics><\/math><\/span>r<\/span><\/span><\/span><\/span>\u3092\u66f8\u304d\u63db\u3048\u308b\u3068\u3001\u6700\u7d42\u7684\u306a\u5fa9\u53f7\u5316\u306e\u5f0f\u304c\u5f97\u3089\u308c\u307e\u3059\u306d\u3002<\/p>\n

      X<\/mi>i<\/mi>\u2212<\/mo>1<\/mn><\/mrow><\/msub>=<\/mo>P<\/mi>(<\/mo>s<\/mi>i<\/mi><\/msub>)<\/mo>Q<\/mi>+<\/mo>R<\/mi>\u2212<\/mo>C<\/mi>(<\/mo>s<\/mi>i<\/mi><\/msub>)<\/mo>.<\/mi><\/mrow>X_{i-1} = P(s_i)Q + R – C(s_i).<\/annotation><\/semantics><\/math><\/span>X<\/span>i<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span>P<\/span>(<\/span>s<\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span>Q<\/span>+<\/span><\/span>R<\/span>\u2212<\/span><\/span>C<\/span>(<\/span>s<\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span>.<\/span><\/span><\/span><\/span><\/span><\/p>\n

      \u4ee5\u4e0a\u304c\u5fa9\u53f7\u5316\u306e\uff11\u30b9\u30c6\u30c3\u30d7\u3067\u3059\u3002\u5fa9\u53f7\u5316\u306e\u30d7\u30ed\u30bb\u30b9\u306f\u3001\u6700\u7d42\u7684\u306bX<\/mi>i<\/mi><\/msub>=<\/mo>0<\/mn><\/mrow>X_i = 0<\/annotation><\/semantics><\/math><\/span>X<\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span>0<\/span><\/span><\/span><\/span>\u306b\u5230\u9054\u3059\u308b\u307e\u3067\u3001\u7e70\u308a\u8fd4\u3057\u7d9a\u3051\u3089\u308c\u307e\u3059\u3002\u305d\u306e\u305f\u3073\u306bs<\/mi>i<\/mi><\/msub><\/mrow>s_i<\/annotation><\/semantics><\/math><\/span>s<\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3092\u8a18\u9332\u3057\u3001\u6700\u7d42\u7684\u306b\u5f97\u3089\u308c\u308b\u6587\u5b57\u5217\u304c\u5b8c\u5168\u306b\u5fa9\u53f7\u5316\u3055\u308c\u305f\u6587\u5b57\u5217\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n

      \u3053\u3053\u3067\u3001\u5fa9\u53f7\u5316\u306f\u7b26\u53f7\u5316\u3068\u306f\u9006\u306e\u9806\u5e8f\u3067\u9032\u3080\u3053\u3068\u306b\u6ce8\u610f\u304c\u5fc5\u8981\u3067\u3059\u3002\u3064\u307e\u308a\u3001(<\/mo>s<\/mi>1<\/mn><\/msub>,<\/mo>s<\/mi>2<\/mn><\/msub>,<\/mo>.<\/mi>.<\/mi>.<\/mi>,<\/mo>s<\/mi>m<\/mi><\/msub>)<\/mo><\/mrow>(s_1, s_2, …, s_m)<\/annotation><\/semantics><\/math><\/span>(<\/span>s<\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span>s<\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span>…<\/span>,<\/span>s<\/span>m<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span>\u3092\u3053\u306e\u9806\u5e8f\u3067\u7b26\u53f7\u5316\u3057\u305f\u5834\u5408\u3001\u30b7\u30f3\u30dc\u30eb\u306f(<\/mo>s<\/mi>m<\/mi><\/msub>,<\/mo>s<\/mi>m<\/mi>\u2212<\/mo>1<\/mn><\/mrow><\/msub>,<\/mo>\u22ef<\/mo>\u2009<\/mtext>,<\/mo>s<\/mi>1<\/mn><\/msub>)<\/mo><\/mrow>(s_m,s_{m-1},\\cdots,s_1)<\/annotation><\/semantics><\/math><\/span>(<\/span>s<\/span>m<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span>s<\/span>m<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span>\u22ef<\/span>,<\/span>s<\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span>\u306e\u9806\u5e8f\u3067\u5fa9\u53f7\u5316\u3055\u308c\u308b\u3068\u3044\u3046\u3053\u3068\u3067\u3059\u3002<\/p>\n

      \u4f8b<\/h2>\n

      \u3067\u306f\u3001\u7c21\u5358\u306a\u4f8b\u984c\u3092\u898b\u3066\u3044\u304d\u307e\u3057\u3087\u3046\u3002<\/p>\n

      \u3053\u3053\u3067\u306f\u3001\u56f31\u306e\u8a2d\u5b9a\u3092\u305d\u306e\u307e\u307e\u7528\u3044\u307e\u3059\u3002\u73fe\u5728\u307e\u3067\u306bX<\/mi>5<\/mn><\/msub>=<\/mo>691<\/mn><\/mrow>X_{5}=691<\/annotation><\/semantics><\/math><\/span>X<\/span>5<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span>691<\/span><\/span><\/span><\/span>\u307e\u3067\u7b26\u53f7\u5316\u3055\u308c\u3066\u3044\u308b\u3068\u3057\u3066\u3001\u3053\u3053\u30676\u756a\u76ee\u306e\u6587\u5b57\u3068\u3057\u3066\u300cc\u300d\u3092\u5727\u7e2e\u3057\u3066\u307f\u307e\u3059\u3002<\/p>\n

      \u4e0a\u8a18\u306e\u8a08\u7b97\u306b\u5f93\u3046\u3068\u3001P<\/mi>(<\/mo>c<\/mi>)<\/mo>=<\/mo>2<\/mn><\/mrow>P(c) = 2<\/annotation><\/semantics><\/math><\/span>P<\/span>(<\/span>c<\/span>)<\/span>=<\/span><\/span>2<\/span><\/span><\/span><\/span>\u3001q<\/mi>=<\/mo>345<\/mn><\/mrow>q = 345<\/annotation><\/semantics><\/math><\/span>q<\/span>=<\/span><\/span>345<\/span><\/span><\/span><\/span>\u3001r<\/mi>=<\/mo>1<\/mn><\/mrow>r= 1<\/annotation><\/semantics><\/math><\/span>r<\/span>=<\/span><\/span>1<\/span><\/span><\/span><\/span>\u3068\u306a\u308b\u3053\u3068\u304c\u308f\u304b\u308b\u3068\u601d\u3044\u307e\u3059\u3002\u3064\u307e\u308a\u3001X<\/mi>6<\/mn><\/msub>=<\/mo>q<\/mi>M<\/mi>+<\/mo>C<\/mi>(<\/mo>c<\/mi>)<\/mo>+<\/mo>r<\/mi>=<\/mo>3458<\/mn><\/mrow>X_6=qM+C(c)+r=3458<\/annotation><\/semantics><\/math><\/span>X<\/span>6<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span>qM<\/span>+<\/span><\/span>C<\/span>(<\/span>c<\/span>)<\/span>+<\/span><\/span>r<\/span>=<\/span><\/span>3458<\/span><\/span><\/span><\/span>\u304c\u5f97\u3089\u308c\u307e\u3059\u3002\u3053\u308c\u3060\u3051\u3067\u5727\u7e2e\u306f\u5b8c\u4e86\u3067\u3059\u3002<\/p>\n

      \u3067\u306f\u3001X<\/mi>6<\/mn><\/msub><\/mrow>X_6<\/annotation><\/semantics><\/math><\/span>X<\/span>6<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u304b\u3089X<\/mi>5<\/mn><\/msub><\/mrow>X_5<\/annotation><\/semantics><\/math><\/span>X<\/span>5<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3068\u6587\u5b57\u300cc\u300d\u3092\u3069\u306e\u3088\u3046\u306b\u5fa9\u53f7\u5316\u3067\u304d\u308b\u3067\u3057\u3087\u3046\u304b\uff1f<\/p>\n

      X<\/mi>6<\/mn><\/msub><\/mrow>X_6<\/annotation><\/semantics><\/math><\/span>X<\/span>6<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3092M<\/mi><\/mrow>M<\/annotation><\/semantics><\/math><\/span>M<\/span><\/span><\/span><\/span>\u3067\u5272\u308b\u3068\u5546Q<\/mi>=<\/mo>q<\/mi>=<\/mo>345<\/mn><\/mrow>Q=q=345<\/annotation><\/semantics><\/math><\/span>Q<\/span>=<\/span><\/span>q<\/span>=<\/span><\/span>345<\/span><\/span><\/span><\/span>\u3068\u4f59\u308aR<\/mi>=<\/mo>8<\/mn><\/mrow>R=8<\/annotation><\/semantics><\/math><\/span>R<\/span>=<\/span><\/span>8<\/span><\/span><\/span><\/span>\u3092\u5f97\u307e\u3059\u3002R<\/mi><\/mrow>R<\/annotation><\/semantics><\/math><\/span>R<\/span><\/span><\/span><\/span>\u304b\u3089\u6587\u5b57\u3068\u4f59\u308ar<\/mi><\/mrow>r<\/annotation><\/semantics><\/math><\/span>r<\/span><\/span><\/span><\/span>\u3092\u5fa9\u53f7\u5316\u3059\u308b\u306b\u306f\u3001\u56f32\u3092\u53c2\u7167\u3057\u3066\u304f\u3060\u3055\u3044\u3002C<\/mi>(<\/mo>c<\/mi>)<\/mo>\u2264<\/mo>R<\/mi>C<\/mi>(<\/mo>d<\/mi>)<\/mo><\/mo><\/mrow>C(c) \\leq R <\/annotation><\/semantics><\/math><\/span>C<\/span>(<\/span>c<\/span>)<\/span>\u2264<\/span><\/span>R<\/span><\/span>C<\/span>(<\/span>d<\/span>)<\/span><\/span><\/span><\/span>\uff08\u5177\u4f53\u7684\u306b\u306f7<\/mn>\u2264<\/mo>8<\/mn>9<\/mn><\/mo><\/mrow>7\\leq 8 <\/annotation><\/semantics><\/math><\/span>7<\/span>\u2264<\/span><\/span>8<\/span><\/span>9<\/span><\/span><\/span><\/span>\uff09\u3067\u3042\u308b\u305f\u3081\u3001R<\/mi><\/mrow>R<\/annotation><\/semantics><\/math><\/span>R<\/span><\/span><\/span><\/span>\u306f\u6587\u5b57\u300cc<\/mi><\/mrow>c<\/annotation><\/semantics><\/math><\/span>c<\/span><\/span><\/span><\/span>\u300d\u306e\u7bc4\u56f2\u5185\u306b\u3042\u308b\u306e\u3067\u3001\u3053\u3053\u3067\u300cc<\/mi><\/mrow>c<\/annotation><\/semantics><\/math><\/span>c<\/span><\/span><\/span><\/span>\u300d\u3092\u5fa9\u53f7\u5316\u3067\u304d\u307e\u3059\u3002<\/span><\/span><\/p>\n

      \u307e\u305f\u3001R<\/mi><\/mrow>R<\/annotation><\/semantics><\/math><\/span>R<\/span><\/span><\/span><\/span>\u306f\u300cc\u300d\u306e\u7bc4\u56f2\u5185\u3067\u50241<\/mn><\/mrow>1<\/annotation><\/semantics><\/math><\/span>1<\/span><\/span><\/span><\/span>\u3092\u6301\u3064\u3053\u3068\u304c\u308f\u304b\u308b\uff08\u56f3\u306e\u30aa\u30ec\u30f3\u30b8\u306e\u90e8\u5206\uff09\u306e\u3067\u3001r<\/mi>=<\/mo>1<\/mn><\/mrow>r=1<\/annotation><\/semantics><\/math><\/span>r<\/span>=<\/span><\/span>1<\/span><\/span><\/span><\/span>\u3067\u3042\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u306d\u3002\u3057\u305f\u304c\u3063\u3066\u3001X<\/mi>5<\/mn><\/msub>=<\/mo>P<\/mi>(<\/mo>c<\/mi>)<\/mo>q<\/mi>+<\/mo>r<\/mi>=<\/mo>691<\/mn><\/mrow>X_{5}=P(c) q + r=691<\/annotation><\/semantics><\/math><\/span>X<\/span>5<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span>P<\/span>(<\/span>c<\/span>)<\/span>q<\/span>+<\/span><\/span>r<\/span>=<\/span><\/span>691<\/span><\/span><\/span><\/span>\u304c\u5f97\u3089\u308c\u308b\u3068\u3044\u3046\u308f\u3051\u3067\u3059\u3002<\/p>\n
      \"\u56f32:
      \u56f32: \u4e0a\u8a18\u306e\u4f8b\u984c\u3067\u306e\u5727\u7e2e\u3068\u89e3\u51cd\u306e\u3046\u3061\u3001\u7bc4\u56f2\u306e\u8a08\u7b97\u306e\u69d8\u5b50\u3002<\/figcaption><\/figure>\n

      \u524d\u306e\u7bc0\u3067\u306f\u3001\u6587\u5b57\u5217\u306b\u95a2\u3059\u308b\u3059\u3079\u3066\u306e\u60c5\u5831\u3092\u542b\u3080\u5de8\u5927\u306a\u6574\u6570\u3092\u4f5c\u6210\u3059\u308b\u3053\u3068\u3092\u4e3b\u306a\u30a2\u30a4\u30c7\u30a2\u3068\u3059\u308brANS\u30b3\u30fc\u30c7\u30c3\u30af\u3092\u7d39\u4ecb\u3057\u307e\u3057\u305f\u3002<\/p>\n

      rANS\u306f\u4e0e\u3048\u3089\u308c\u305f\u78ba\u7387\u5206\u5e03\u306b\u5bfe\u3057\u3066\u6700\u9069\u306a\u30a8\u30f3\u30c8\u30ed\u30d4\u30fc\u7b26\u53f7\u5316\u3092\u5b9f\u73fe\u3059\u308b\u3053\u3068\u3067\u77e5\u3089\u308c\u3066\u3044\u307e\u3059\u304c\u3001\u6587\u5b57\u5217\u306e\u30b5\u30a4\u30ba\u304c\u5927\u304d\u304f\u306a\u308b\u306b\u3064\u308c\u3066\u6025\u901f\u306b\u5b9f\u7528\u7684\u3067\u306a\u304f\u306a\u3063\u3066\u3057\u307e\u3044\u307e\u3059\u3002<\/p>\n

      \u3068\u3044\u3046\u306e\u3082\u3001\u307e\u3059\u307e\u3059\u5927\u304d\u304f\u306a\u308b\u6574\u6570\u306b\u5bfe\u3057\u3066\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u9664\u7b97\u3092\u5b9f\u884c\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u3001\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u9664\u7b97\u306f\u6574\u6570\u304c\u4f55\u767e\u6841\u3001\u4f55\u5343\u6841\u3068\u5927\u304d\u304f\u306a\u308c\u3070\u8a08\u7b97\u304c\u307b\u307c\u4e0d\u53ef\u80fd\u306b\u306a\u3063\u3066\u3057\u307e\u3046\u306e\u3067\u3059\u3002<\/p>\n

      \u3053\u306e\u554f\u984c\u3092\u89e3\u6c7a\u7b56\u3068\u3057\u3066\u3001\u5404\u72b6\u614b\u306e\u5024X<\/mi>i<\/mi><\/msub><\/mrow>X_i<\/annotation><\/semantics><\/math><\/span>X<\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3092\u5206\u89e3\u3057\u3066\u3001\u9069\u5ea6\u306b\u5c0f\u3055\u304f\u4fdd\u3064\u3068\u3044\u3046\u3053\u3068\u304c\u8003\u3048\u3089\u308c\u307e\u3059\u3002\u3053\u308c\u306f\u3001\u30b9\u30c8\u30ea\u30fc\u30df\u30f3\u30b0rANS\u3068\u3088\u3070\u308c\u308b\u3001rANS\u306b\u5c11\u3057\u5909\u66f4\u3092\u52a0\u3048\u305f\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306b\u3088\u3063\u3066\u5b9f\u73fe\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n

      \u3053\u306e\u7bc0\u3067\u306f\u30b9\u30c8\u30ea\u30fc\u30df\u30f3\u30b0rANS\u306b\u3064\u3044\u3066\u89e3\u8aac\u3057\u3066\u3044\u304d\u307e\u3059\u3002<\/p>\n

      \u30b9\u30c8\u30ea\u30fc\u30df\u30f3\u30b0\u7b26\u53f7\u5316<\/h2>\n

      \u307e\u305a\u3001\u6b63\u306e\u6574\u6570k<\/mi><\/mrow>k<\/annotation><\/semantics><\/math><\/span>k<\/span><\/span><\/span><\/span>\u3068l<\/mi><\/mrow>l<\/annotation><\/semantics><\/math><\/span>l<\/span><\/span><\/span><\/span>\u3092\u9078\u629e\u3057\u307e\u3059\u3002\u3053\u306e\u9078\u629e\u306f\u5b8c\u5168\u306b\u81ea\u7531\u3067\u3059\u304c\u3001\u9078\u629e\u3059\u308b\u306b\u3042\u305f\u3063\u3066\u306f\u3044\u304f\u3064\u304b\u306e\u6307\u6a19\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n

      \u307e\u305ak<\/mi><\/mrow>k<\/annotation><\/semantics><\/math><\/span>k<\/span><\/span><\/span><\/span>\u306f\u3001\u30b9\u30c8\u30ea\u30fc\u30e0\u306b\u9001\u4fe1\u3059\u308b\u5404\u8ee2\u9001\u306e\u30d3\u30c3\u30c8\u6570\u3092\u793a\u3057\u3066\u3044\u307e\u3059\u3002\u6700\u3082\u5358\u7d14\u306a\u5b9f\u88c5\u3067\u306fk<\/mi>=<\/mo>1<\/mn><\/mrow>k=1<\/annotation><\/semantics><\/math><\/span>k<\/span>=<\/span><\/span>1<\/span><\/span><\/span><\/span>\u306b\u8a2d\u5b9a\u3057\u3001\u30d0\u30a4\u30c8\u30b9\u30c8\u30ea\u30fc\u30e0\u306e\u5834\u5408\u306fk<\/mi>=<\/mo>8<\/mn><\/mrow>k=8<\/annotation><\/semantics><\/math><\/span>k<\/span>=<\/span><\/span>8<\/span><\/span><\/span><\/span>\u306b\u8a2d\u5b9a\u3059\u308b\u306e\u304c\u826f\u3044\u3067\u3057\u3087\u3046\u3002<\/p>\n

      l<\/mi><\/mrow>l<\/annotation><\/semantics><\/math><\/span>l<\/span><\/span><\/span><\/span>\u306fX<\/mi>i<\/mi><\/msub><\/mrow>X_i<\/annotation><\/semantics><\/math><\/span>X<\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3092\u3069\u308c\u3060\u3051\u5c0f\u3055\u304f\u4fdd\u3064\u304b\u3092\u793a\u3059\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u30d1\u30e9\u30e1\u30fc\u30bf\u3067\u3042\u308a\u3001l<\/mi><\/mrow>l<\/annotation><\/semantics><\/math><\/span>l<\/span><\/span><\/span><\/span>\u306e\u5024\u304c\u9ad8\u3044\u307b\u3069\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u9045\u304f\u306a\u308a\u307e\u3059\u304c\u3001\u5727\u7e2e\u52b9\u7387\u306f\u5411\u4e0a\u3057\u307e\u3059\u3002<\/p>\n

      \u3053\u3053\u3067\u89e3\u8aac\u3059\u308b\u30b9\u30c8\u30ea\u30fc\u30e0rANS\u306f\u3001\u5404\u30b9\u30c6\u30c3\u30d7\u306b\u304a\u3044\u3066\u72b6\u614b\u306e\u5024\u304cl<\/mi>M<\/mi><\/mrow>lM<\/annotation><\/semantics><\/math><\/span>lM<\/span><\/span><\/span><\/span>\u30682<\/mn>k<\/mi><\/msup>l<\/mi>M<\/mi>\u2212<\/mo>1<\/mn><\/mrow>2^klM-1<\/annotation><\/semantics><\/math><\/span>2<\/span>k<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>lM<\/span>\u2212<\/span><\/span>1<\/span><\/span><\/span><\/span>\u306e\u9593\u306b\u3042\u308b\u3053\u3068\u3092\u4fdd\u8a3c\u3057\u3066\u304f\u308c\u308b\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3067\u3059\u3002\u3064\u307e\u308a\u3001<\/p>\n

      I<\/mi>=<\/mo>{<\/mo>l<\/mi>M<\/mi>,<\/mo>\u22ef<\/mo>\u2009<\/mtext>,<\/mo>2<\/mn>k<\/mi><\/msup>l<\/mi>M<\/mi>\u2212<\/mo>1<\/mn>}<\/mo><\/mrow>I=\\{lM,\\cdots,2^k l M-1\\}<\/annotation><\/semantics><\/math><\/span>I<\/span>=<\/span><\/span>{<\/span>lM<\/span>,<\/span>\u22ef<\/span>,<\/span>2<\/span>k<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>lM<\/span>\u2212<\/span><\/span>1<\/span>}<\/span><\/span><\/span><\/span><\/span><\/p>\n

      \u3068\u5b9a\u7fa9\u3057\u305f\u5834\u5408\u3001\u5e38\u306bX<\/mi>i<\/mi><\/msub>\u2208<\/mo>I<\/mi><\/mrow>X_i \\in I<\/annotation><\/semantics><\/math><\/span>X<\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2208<\/span><\/span>I<\/span><\/span><\/span><\/span>\u3068\u306a\u308b\u3053\u3068\u3092\u4fdd\u8a3c\u3057\u3066\u304f\u308c\u307e\u3059\u3002\u4f8b\u3048\u3070\u300164-bit\u306e\u975e\u8ca0\u6574\u6570\u3092\u7528\u3044\u308b\u5834\u5408\u30012<\/mn>k<\/mi><\/msup>l<\/mi>M<\/mi><\/mrow>2^klM<\/annotation><\/semantics><\/math><\/span>2<\/span>k<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>lM<\/span><\/span><\/span><\/span>\u304c2<\/mn>64<\/mn><\/msup><\/mrow>2^{64}<\/annotation><\/semantics><\/math><\/span>2<\/span>64<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3092\u8d85\u3048\u306a\u3044\u3088\u3046\u306brANS\u3092\u8a2d\u8a08\u3059\u308b\u3053\u3068\u306f\u5b9f\u88c5\u306b\u304a\u3044\u3066\u3072\u3068\u3064\u306e\u91cd\u8981\u306a\u30dd\u30a4\u30f3\u30c8\u3067\u3042\u308b\u3068\u8a00\u3048\u307e\u3059\u3002<\/p>\n

      \u30b9\u30c8\u30ea\u30fc\u30df\u30f3\u30b0rANS\u306e\u8003\u3048\u65b9\u81ea\u4f53\u306f\u975e\u5e38\u306b\u5358\u7d14\u3067\u3001\u5404\u30b9\u30c6\u30c3\u30d7i<\/mi><\/mrow>i<\/annotation><\/semantics><\/math><\/span>i<\/span><\/span><\/span><\/span>\u306b\u304a\u3044\u3066\u3001E<\/mi>(<\/mo>X<\/mi>i<\/mi>\u2212<\/mo>1<\/mn><\/mrow><\/msub>,<\/mo>s<\/mi>)<\/mo><\/mrow>E(X_{i-1},s)<\/annotation><\/semantics><\/math><\/span>E<\/span>(<\/span>X<\/span>i<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span>s<\/span>)<\/span><\/span><\/span><\/span>\u304c\u7bc4\u56f2I<\/mi><\/mrow>I<\/annotation><\/semantics><\/math><\/span>I<\/span><\/span><\/span><\/span>\u304b\u3089\u5916\u308c\u305d\u3046\u306b\u306a\u308b\u3068\u304d\u306f\u72b6\u614bX<\/mi>i<\/mi>\u2212<\/mo>1<\/mn><\/mrow><\/msub><\/mrow>X_{i-1}<\/annotation><\/semantics><\/math><\/span>X<\/span>i<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u30922<\/mn>k<\/mi><\/msup><\/mrow>2^k<\/annotation><\/semantics><\/math><\/span>2<\/span>k<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3067\u5272\u308a\u3001\u4f59\u308a\u306ek<\/mi><\/mrow>k<\/annotation><\/semantics><\/math><\/span>k<\/span><\/span><\/span><\/span>\u6570\u3092\u30b9\u30c8\u30ea\u30fc\u30e0\u306b\u51fa\u529b\u3057\u3066\u3057\u307e\u3046\u3053\u3068\u3067\u3001X<\/mi>i<\/mi><\/msub><\/mrow>X_i<\/annotation><\/semantics><\/math><\/span>X<\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3092\u5e38\u306bI<\/mi><\/mrow>I<\/annotation><\/semantics><\/math><\/span>I<\/span><\/span><\/span><\/span>\u306e\u5185\u90e8\u306b\u4fdd\u3063\u3066\u3044\u307e\u3059\u3002<\/p>\n
      \"\u56f33\uff1a\u30b9\u30c8\u30ea\u30fc\u30df\u30f3\u30b0rANS\u304c\u30ab\u30d5\u30ab\u306e\u5f15\u7528\u3092\u7b26\u53f7\u5316\u3059\u308b\u69d8\u5b50\u3002\u72b6\u614b\u306e\u5024\uff08State
      \u56f33\uff1a\u30b9\u30c8\u30ea\u30fc\u30df\u30f3\u30b0rANS\u304c\u30ab\u30d5\u30ab\u306e\u5f15\u7528\u3092\u7b26\u53f7\u5316\u3059\u308b\u69d8\u5b50\u3002\u72b6\u614b\u306e\u5024\uff08State Value\uff09\u3068\u30b9\u30c8\u30ea\u30fc\u30e0\uff08Stream\uff09\u306f16\u9032\u6570\u3067\u8868\u3055\u308c\u3066\u3044\u308b\u3002\u3064\u307e\u308a\u3001\u3082\u3068\u306e\u30c7\u30fc\u30bf\u304c\uff11\u6587\u5b57\uff11\u30d0\u30a4\u30c8\u3067\u4fdd\u5b58\u3057\u3066\u3044\u308b\u3068\u3059\u308c\u3070\u3001\u3053\u3053\u3067\u306e\u5727\u7e2e\u7387\u306f50\uff05\u307b\u3069\u306b\u306a\u308b\u3002\u72b6\u614b\u306e\u5024\u304c\u8d64\u3044\u6841\u3092\u6301\u3064\u3068\u304d\u306fI\u306e\u4e2d\u306b\u3042\u308b\u3053\u3068\u3092\u610f\u5473\u3059\u308b\u3002\u56f3\u304b\u3089\u72b6\u614b\u306e\u5024\u304c\u5e38\u306bI\u306e\u4e2d\u306b\u3001\u3072\u3044\u3066\u306f32\u30d3\u30c3\u30c8\u4ee5\u4e0b\u306b\u6291\u3048\u3089\u308c\u3066\u3044\u308b\u3053\u3068\u304c\u308f\u304b\u308b\u3002<\/figcaption><\/figure>\n

      \u3055\u3066\u3001\u72b6\u614b\u306e\u5024\u304cI<\/mi><\/mrow>I<\/annotation><\/semantics><\/math><\/span>I<\/span><\/span><\/span><\/span>\u306e\u7bc4\u56f2\u304b\u3089\u5916\u308c\u3088\u3046\u3068\u3057\u3066\u3044\u308b\u3053\u3068\u3092\u305d\u3082\u305d\u3082\u3069\u306e\u3088\u3046\u306b\u3057\u3066\u77e5\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u306e\u3067\u3057\u3087\u3046\u304b\uff1f\u8a00\u3044\u63db\u3048\u308c\u3070\u3001\u3069\u306e\u72b6\u614b\u5024X<\/mi><\/mrow>X<\/annotation><\/semantics><\/math><\/span>X<\/span><\/span><\/span><\/span>\u3068\u6587\u5b57s<\/mi>\u2208<\/mo>S<\/mi><\/mrow>s \\in S<\/annotation><\/semantics><\/math><\/span>s<\/span>\u2208<\/span><\/span>S<\/span><\/span><\/span><\/span>\u306e\u3068\u304dE<\/mi>(<\/mo>X<\/mi>,<\/mo>s<\/mi>)<\/mo>\u2208<\/mo>I<\/mi><\/mrow>E(X,s) \\in I<\/annotation><\/semantics><\/math><\/span>E<\/span>(<\/span>X<\/span>,<\/span>s<\/span>)<\/span>\u2208<\/span><\/span>I<\/span><\/span><\/span><\/span>\u3068\u306a\u308b\u306e\u3067\u3057\u3087\u3046\u304b\uff1f\u3053\u306e\u554f\u306b\u7b54\u3048\u308b\u306b\u306f\u3001\u6b21\u306e\u3088\u3046\u306b\u5b9a\u7fa9\u3055\u308c\u308b\u96c6\u5408<\/p>\n

      I<\/mi>s<\/mi><\/msub>=<\/mo>E<\/mi>s<\/mi>\u2212<\/mo>1<\/mn><\/mrow><\/msubsup>(<\/mo>I<\/mi>)<\/mo><\/mrow>I_s=E_s^{-1}(I)<\/annotation><\/semantics><\/math><\/span>I<\/span>s<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span>E<\/span>s<\/span><\/span><\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>I<\/span>)<\/span><\/span><\/span><\/span><\/span><\/p>\n

      \u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u77e5\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n

      \u3053\u306e\u96c6\u5408\u3092\u8a08\u7b97\u3059\u308b\u306e\u306b\u5f79\u7acb\u3064\u4e8b\u5b9f\u3068\u3057\u3066\u3001\u95a2\u6570E<\/mi>s<\/mi><\/msub><\/mrow>E_s<\/annotation><\/semantics><\/math><\/span>E<\/span>s<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u304c\u5358\u8abf\u5897\u52a0\u3067\u3042\u308b\u3053\u3068\u304c\u3042\u3052\u3089\u308c\u307e\u3059\u3002\u3064\u307e\u308a\u3001\u5165\u529b\u304c\u5927\u304d\u304f\u306a\u308c\u3070\u306a\u308b\u307b\u3069\u3001\u51fa\u529b\u3082\u5927\u304d\u304f\u306a\u308b\u3068\u3044\u3046\u6027\u8cea\u3092\u6301\u3063\u3066\u3044\u308b\u306e\u3067\u3059\uff08\u3053\u308c\u306f\u7c21\u5358\u306b\u78ba\u304b\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\uff09\u3002<\/p>\n

      \u3053\u306e\u4e8b\u5b9f\u3055\u3048\u3042\u308c\u3070\u3001L<\/mi>s<\/mi><\/msub>=<\/mo>min<\/mi>\u2061<\/mo>{<\/mo>L<\/mi>:<\/mo>E<\/mi>s<\/mi><\/msub>(<\/mo>L<\/mi>)<\/mo>\u2265<\/mo>l<\/mi>M<\/mi>}<\/mo><\/mrow>L_s = \\min \\{L: E_s(L)\\geq lM \\}<\/annotation><\/semantics><\/math><\/span>L<\/span>s<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span>min<\/span>{<\/span>L<\/span>:<\/span><\/span>E<\/span>s<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>L<\/span>)<\/span>\u2265<\/span><\/span>lM<\/span>}<\/span><\/span><\/span><\/span>\u304a\u3088\u3073H<\/mi>s<\/mi><\/msub>=<\/mo>max<\/mi>\u2061<\/mo>{<\/mo>H<\/mi>:<\/mo>E<\/mi>s<\/mi><\/msub>(<\/mo>H<\/mi>)<\/mo>\u2264<\/mo>2<\/mn>k<\/mi><\/msup>l<\/mi>M<\/mi>\u2212<\/mo>1<\/mn>}<\/mo><\/mrow>H_s = \\max\\{H:E_s(H)\\leq2^klM-1\\}<\/annotation><\/semantics><\/math><\/span>H<\/span>s<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span>max<\/span>{<\/span>H<\/span>:<\/span><\/span>E<\/span>s<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>H<\/span>)<\/span>\u2264<\/span><\/span>2<\/span>k<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>lM<\/span>\u2212<\/span><\/span>1<\/span>}<\/span><\/span><\/span><\/span>\u306e2\u3064\u306e\u6570\u3055\u3048\u308f\u304b\u308c\u3070\u3082\u3046\u4e0a\u8a18\u306e\u554f\u306f\u89e3\u6c7a\u3057\u307e\u3059\u3002\u306a\u305c\u306a\u3089\u3001\u5358\u8abf\u6027\u306b\u3088\u308a\u3001L<\/mi>s<\/mi><\/msub>\u2264<\/mo>X<\/mi>\u2264<\/mo>H<\/mi>s<\/mi><\/msub><\/mrow>L_s \\leq X \\leq H_s<\/annotation><\/semantics><\/math><\/span>L<\/span>s<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2264<\/span><\/span>X<\/span>\u2264<\/span><\/span>H<\/span>s<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3092\u6301\u3064\u4efb\u610f\u306e\u6570X<\/mi><\/mrow>X<\/annotation><\/semantics><\/math><\/span>X<\/span><\/span><\/span><\/span>\u3082I<\/mi>s<\/mi><\/msub><\/mrow> I_s<\/annotation><\/semantics><\/math><\/span>I<\/span>s<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u306b\u542b\u307e\u308c\u308b\u3053\u3068\u304c\u308f\u304b\u308b\u304b\u3089\u3067\u3059\u3002<\/p>\n

      \u3067\u306f\u3001L<\/mi>s<\/mi><\/msub><\/mrow>L_s<\/annotation><\/semantics><\/math><\/span>L<\/span>s<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3068H<\/mi>s<\/mi><\/msub><\/mrow>H_s<\/annotation><\/semantics><\/math><\/span>H<\/span>s<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u306e\u5b9f\u969b\u306e\u5024\u306f\u4f55\u3067\u3057\u3087\u3046\u304b\uff1f\u3082\u3057\u304a\u6642\u9593\u304c\u3042\u308c\u3070\u3001\u3068\u3066\u3082\u3044\u3044\u6f14\u7fd2\u306b\u306a\u308b\u3068\u601d\u3044\u307e\u3059\u306e\u3067\u3001\u305c\u3072\u3054\u81ea\u8eab\u3067\u8a08\u7b97\u3057\u3066\u307f\u3066\u304f\u3060\u3055\u3044\uff01<\/p>\n

      \u2026 \u3069\u3046\u3067\u3057\u305f\u3067\u3057\u3087\u3046\u304b\uff1f\u305d\u308c\u3067\u306f\u7b54\u3048\u5408\u308f\u305b\u3092\u3057\u3066\u3044\u304d\u307e\u3059\u3002\u7d50\u679c\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n

      I<\/mi>s<\/mi><\/msub>=<\/mo>{<\/mo>L<\/mi>s<\/mi><\/msub>,<\/mo>\u22ef<\/mo>\u2009<\/mtext>,<\/mo>H<\/mi>s<\/mi><\/msub>}<\/mo>=<\/mo>{<\/mo>l<\/mi>P<\/mi>(<\/mo>s<\/mi>)<\/mo>,<\/mo>\u22ef<\/mo>\u2009<\/mtext>,<\/mo>2<\/mn>k<\/mi><\/msup>l<\/mi>P<\/mi>(<\/mo>s<\/mi>)<\/mo>\u2212<\/mo>1<\/mn>}<\/mo>.<\/mi><\/mrow>I_s=\\{L_s,\\cdots, H_s\\} = \\{lP(s),\\cdots,2^k lP(s)-1\\}.<\/annotation><\/semantics><\/math><\/span>I<\/span>s<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span>{<\/span>L<\/span>s<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span>\u22ef<\/span>,<\/span>H<\/span>s<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>}<\/span>=<\/span><\/span>{<\/span>lP<\/span>(<\/span>s<\/span>)<\/span>,<\/span>\u22ef<\/span>,<\/span>2<\/span>k<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>lP<\/span>(<\/span>s<\/span>)<\/span>\u2212<\/span><\/span>1<\/span>}<\/span>.<\/span><\/span><\/span><\/span><\/span><\/p>\n

      I<\/mi>s<\/mi><\/msub><\/mrow>I_s<\/annotation><\/semantics><\/math><\/span>I<\/span>s<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u306b\u5bfe\u3059\u308b\u3053\u306e\u3059\u3063\u304d\u308a\u3068\u3057\u305f\u5f0f\u306b\u306a\u308b\u306e\u306f\u3001\u5b9f\u306fI<\/mi><\/mrow>I<\/annotation><\/semantics><\/math><\/span>I<\/span><\/span><\/span><\/span>\u306f\u305d\u306e\u3088\u3046\u306b\u8a2d\u8a08\u3055\u308c\u3066\u3044\u308b\u304a\u304b\u3052\u306a\u306e\u3067\u3059\uff01<\/p>\n

      \u3057\u305f\u304c\u3063\u3066\u3001s<\/mi><\/mrow>s<\/annotation><\/semantics><\/math><\/span>s<\/span><\/span><\/span><\/span>\u3092\u7b26\u53f7\u5316\u3057\u3088\u3046\u3068\u3059\u308b\u3068\u304d\u306b\u72b6\u614b\u5024\u304c\u4e0a\u8a18\u306eI<\/mi>s<\/mi><\/msub><\/mrow>I_s<\/annotation><\/semantics><\/math><\/span>I<\/span>s<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u306e\u5185\u90e8\u306b\u3042\u308c\u3070\u3001\u7d50\u679c\u3068\u3057\u3066\u5f97\u3089\u308c\u308b\u72b6\u614b\u5024X<\/mi>i<\/mi><\/msub><\/mrow>X_i<\/annotation><\/semantics><\/math><\/span>X<\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u306f\u6c7a\u3057\u3066\u30aa\u30fc\u30d0\u30fc\u30d5\u30ed\u30fc\u3057\u306a\u3044\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3057\u305f\u306d\u3002<\/p>\n

      \u3053\u308c\u3067\u3044\u3088\u3044\u3088\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u8aac\u660e\u3059\u308b\u6e96\u5099\u304c\u6574\u3044\u307e\u3057\u305f\u3002\u72b6\u614bX<\/mi>i<\/mi>\u2212<\/mo>1<\/mn><\/mrow><\/msub><\/mrow>X_{i-1}<\/annotation><\/semantics><\/math><\/span>X<\/span>i<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u304c\u4e0e\u3048\u3089\u308c\u305f\u3068\u304d\u3001\u30b7\u30f3\u30dc\u30ebs<\/mi>i<\/mi><\/msub><\/mrow>s_i<\/annotation><\/semantics><\/math><\/span>s<\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u306f\u6b21\u306e\u3088\u3046\u306b\u7b26\u53f7\u5316\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n

      <\/mstyle><\/mtd>while\u00a0<\/mtext>X<\/mi>i<\/mi>\u2212<\/mo>1<\/mn><\/mrow><\/msub>\u2208\u0338<\/mo>I<\/mi>s<\/mi>i<\/mi><\/msub><\/msub>:<\/mo><\/mrow><\/mstyle><\/mtd><\/mtr><\/mstyle><\/mtd>\u2005\u200a<\/mtext>\u2005\u200a<\/mtext>\u2005\u200a<\/mtext>\u2005\u200a<\/mtext>output\u00a0<\/mtext>X<\/mi>i<\/mi>\u2212<\/mo>1<\/mn><\/mrow><\/msub>m<\/mi>o<\/mi>d<\/mi><\/mrow>\u2009<\/mtext>\u2009<\/mtext>2<\/mn>k<\/mi><\/msup><\/mrow><\/mstyle><\/mtd><\/mtr><\/mstyle><\/mtd>\u2005\u200a<\/mtext>\u2005\u200a<\/mtext>\u2005\u200a<\/mtext>\u2005\u200a<\/mtext>X<\/mi>i<\/mi>\u2212<\/mo>1<\/mn><\/mrow><\/msub>\u2190<\/mo>\u230a<\/mo>X<\/mi>i<\/mi>\u2212<\/mo>1<\/mn><\/mrow><\/msub>\/<\/mi>2<\/mn>k<\/mi><\/msup>\u230b<\/mo><\/mrow><\/mstyle><\/mtd><\/mtr><\/mstyle><\/mtd>X<\/mi>i<\/mi><\/msub>=<\/mo>E<\/mi>(<\/mo>s<\/mi>i<\/mi><\/msub>,<\/mo>X<\/mi>i<\/mi>\u2212<\/mo>1<\/mn><\/mrow><\/msub>)<\/mo><\/mrow><\/mstyle><\/mtd><\/mtr><\/mtable>\\begin{align}\n&\\text{while } X_{i-1} \\not \\in I_{s_i} : \\\\\n&\\;\\;\\;\\;\\text{output } X_{i-1} \\mod 2^k \\\\\n&\\;\\;\\;\\;X_{i-1} \\leftarrow \\lfloor X_{i-1} \/ 2^k \\rfloor \\\\\n&X_i = E(s_i,X_{i-1})\n\\end{align}\n<\/annotation><\/semantics><\/math><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span>while\u00a0<\/span><\/span>X<\/span>i<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\ue020<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2208<\/span>I<\/span>s<\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>:<\/span><\/span><\/span>output\u00a0<\/span><\/span>X<\/span>i<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>mod<\/span><\/span><\/span>2<\/span>k<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>X<\/span>i<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2190<\/span>\u230a<\/span>X<\/span>i<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\/<\/span>2<\/span>k<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u230b<\/span><\/span><\/span>X<\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span>E<\/span>(<\/span>s<\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span>X<\/span>i<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

      \u6b8b\u308b\u7591\u554f\u306f\u305f\u3060\u4e00\u3064\u3067\u3059\u3002while\u30eb\u30fc\u30d7\u304c\u6709\u9650\u306e\u30b9\u30c6\u30c3\u30d7\u3067\u7d42\u4e86\u3059\u308b\u3053\u3068\u3092\u3069\u306e\u3088\u3046\u306b\u62c5\u4fdd\u3067\u304d\u308b\u306e\u3067\u3057\u3087\u3046\u304b\uff1f2<\/mn>k<\/mi><\/msup><\/mrow>2^k<\/annotation><\/semantics><\/math><\/span>2<\/span>k<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u306b\u3088\u308b\u9664\u7b97\u304cI<\/mi>s<\/mi>i<\/mi><\/msub><\/msub><\/mrow>I_{s_i}<\/annotation><\/semantics><\/math><\/span>I<\/span>s<\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3092\u98db\u3073\u8d8a\u3048\u3066\u3057\u307e\u3046\u5834\u5408\u306f\u7121\u9650\u30eb\u30fc\u30d7\u62c5\u3063\u3066\u3057\u307e\u3044\u307e\u3059\u304c\u3001\u305d\u306e\u5fc3\u914d\u306f\u306a\u3044\u306e\u3067\u3057\u3087\u3046\u304b\uff1f<\/p>\n

      \u5b9f\u306f\u30012<\/mn>k<\/mi><\/msup><\/mrow>2^k<\/annotation><\/semantics><\/math><\/span>2<\/span>k<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u306b\u3088\u308b\u9664\u7b97\u306f\u533a\u9593I<\/mi>s<\/mi>i<\/mi><\/msub><\/msub><\/mrow>I_{s_i}<\/annotation><\/semantics><\/math><\/span>I<\/span>s<\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3092\u98db\u3073\u8d8a\u308b\u3053\u3068\u306f\u6c7a\u3057\u3066\u3042\u308a\u307e\u305b\u3093\u3002\u3053\u308c\u3082\u3001I<\/mi><\/mrow>I<\/annotation><\/semantics><\/math><\/span>I<\/span><\/span><\/span><\/span>\u306e\u8a2d\u8a08\u306e\u304a\u304b\u3052\u3067\u3059\u3002\u3082\u3057\u533a\u9593I<\/mi>s<\/mi>i<\/mi><\/msub><\/msub><\/mrow>I_{s_i}<\/annotation><\/semantics><\/math><\/span>I<\/span>s<\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3092\u98db\u3073\u8d8a\u3048\u308b\u72b6\u614b\u5024\u304c\u5b58\u5728\u3059\u308b\u3068\u3059\u308b\u306a\u3089\u3070\u3001I<\/mi>s<\/mi>i<\/mi><\/msub><\/msub>\u228a<\/mo>{<\/mo>X<\/mi>,<\/mo>\u22ef<\/mo>\u2009<\/mtext>,<\/mo>2<\/mn>k<\/mi><\/msup>X<\/mi>}<\/mo><\/mrow>I_{s_i}\\subsetneq\\{X,\\cdots,2^kX\\}<\/annotation><\/semantics><\/math><\/span>I<\/span>s<\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u228a<\/span><\/span>{<\/span>X<\/span>,<\/span>\u22ef<\/span>,<\/span>2<\/span>k<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>X<\/span>}<\/span><\/span><\/span><\/span>\u3092\u6e80\u305f\u3059\u6574\u6570X<\/mi><\/mrow>X<\/annotation><\/semantics><\/math><\/span>X<\/span><\/span><\/span><\/span>\u304c\u5b58\u5728\u3057\u306a\u3051\u308c\u3070\u306a\u3089\u306a\u304f\u306a\u308a\u307e\u3059\u3002\u3053\u308c\u306fl<\/mi>P<\/mi>(<\/mo>s<\/mi>i<\/mi><\/msub>)<\/mo>X<\/mi>\u2264<\/mo>l<\/mi>P<\/mi>(<\/mo>s<\/mi>i<\/mi><\/msub>)<\/mo><\/mo><\/mrow>lP(s_i)<\/annotation><\/semantics><\/math><\/span>lP<\/span>(<\/span>s<\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span>X<\/span>\u2264<\/span><\/span>lP<\/span>(<\/span>s<\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span>\u307e\u305f\u306fl<\/mi>P<\/mi>(<\/mo>s<\/mi>i<\/mi><\/msub>)<\/mo>\u2264<\/mo>X<\/mi>l<\/mi>P<\/mi>(<\/mo>s<\/mi>i<\/mi><\/msub>)<\/mo><\/mo><\/mrow>lP(s_i) \\leq X <\/annotation><\/semantics><\/math><\/span>lP<\/span>(<\/span>s<\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span>\u2264<\/span><\/span>X<\/span><\/span>lP<\/span>(<\/span>s<\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span>\u3092\u610f\u5473\u3057\u307e\u3059\u304c\u3001\u3069\u3061\u3089\u306e\u5834\u5408\u3082\u6c7a\u3057\u3066\u8d77\u3053\u308a\u5f97\u306a\u3044\u3068\u3044\u3046\u306e\u306f\u81ea\u660e\u306a\u3053\u3068\u3067\u3059\u3088\u306d\u3002\u3053\u308c\u306f\u77db\u76fe\u3068\u306a\u308a\u307e\u3059\u304b\u3089\u3001\u533a\u9593I<\/mi>s<\/mi>i<\/mi><\/msub><\/msub><\/mrow>I_{s_i}<\/annotation><\/semantics><\/math><\/span>I<\/span>s<\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3092\u98db\u3073\u8d8a\u3048\u308b\u304b\u3082\u3057\u308c\u306a\u3044\u3068\u3044\u3046\u524d\u8ff0\u306e\u5fc3\u914d\u306f\u675e\u6182\u3067\u3042\u3063\u305f\u3068\u3044\u3046\u308f\u3051\u3067\u3059\u3002<\/span><\/span><\/p>\n

      \u30b9\u30c8\u30ea\u30fc\u30df\u30f3\u30b0\u5fa9\u53f7\u5316<\/h2>\n

      \u666e\u901a\u306erANS\u540c\u69d8\u3001\u5fa9\u53f7\u5316\u306f\u7b26\u53f7\u5316\u306e\u9006\u306e\u64cd\u4f5c\u306b\u3088\u3063\u3066\u884c\u308f\u308c\u307e\u3059\u3002\u5404\u6642\u523bi<\/mi>\u2208<\/mo>{<\/mo>1<\/mn>,<\/mo>\u22ef<\/mo>\u2009<\/mtext>,<\/mo>m<\/mi>}<\/mo><\/mrow>i\\in\\{1,\\cdots,m\\}<\/annotation><\/semantics><\/math><\/span>i<\/span>\u2208<\/span><\/span>{<\/span>1<\/span>,<\/span>\u22ef<\/span>,<\/span>m<\/span>}<\/span><\/span><\/span><\/span>\u306b\u304a\u3044\u3066\u3001\u524d\u306e\u7bc0\u3067\u8aac\u660e\u3057\u305f\u666e\u901a\u306erANS\u5fa9\u53f7\u5316\u30d7\u30ed\u30bb\u30b9\u3092\u4f7f\u7528\u3057\u3066\u3001X<\/mi>i<\/mi><\/msub><\/mrow>X_i<\/annotation><\/semantics><\/math><\/span>X<\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u304b\u3089\u6587\u5b57s<\/mi>i<\/mi><\/msub><\/mrow>s_i<\/annotation><\/semantics><\/math><\/span>s<\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3068X<\/mi>i<\/mi>\u2212<\/mo>1<\/mn><\/mrow><\/msub><\/mrow>X_{i-1}<\/annotation><\/semantics><\/math><\/span>X<\/span>i<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3092\u5fa9\u53f7\u5316\u3059\u308b\u3053\u3068\u304b\u3089\u59cb\u3081\u307e\u3059\u3002<\/p>\n

      \u6587\u5b57\u3092\u5fa9\u53f7\u5316\u3057\u305f\u5f8c\u3001\u72b6\u614bX<\/mi>i<\/mi>\u2212<\/mo>1<\/mn><\/mrow><\/msub><\/mrow>X_{i-1}<\/annotation><\/semantics><\/math><\/span>X<\/span>i<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u304cI<\/mi><\/mrow>I<\/annotation><\/semantics><\/math><\/span>I<\/span><\/span><\/span><\/span>\u306e\u4e0b\u9650k<\/mi>M<\/mi><\/mrow>kM<\/annotation><\/semantics><\/math><\/span>k<\/span>M<\/span><\/span><\/span><\/span>\u3092\u4e0b\u56de\u308b\u5834\u5408\u3001\u7b26\u53f7\u5316\u3055\u308c\u305f\u30d3\u30c3\u30c8\u30b9\u30c8\u30ea\u30fc\u30e0\u304b\u3089\u8ffd\u52a0\u306ek<\/mi><\/mrow>k<\/annotation><\/semantics><\/math><\/span>k<\/span><\/span><\/span><\/span>\u30d3\u30c3\u30c8\u3092\u8aad\u307f\u8fbc\u3093\u30672<\/mn>k<\/mi><\/msup>X<\/mi>i<\/mi>\u2212<\/mo>1<\/mn><\/mrow><\/msub><\/mrow>2^kX_{i-1}<\/annotation><\/semantics><\/math><\/span>2<\/span>k<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>X<\/span>i<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u306b\u52a0\u3048\u3001\u305d\u308c\u3092\u65b0\u305f\u306bX<\/mi>i<\/mi>\u2212<\/mo>1<\/mn><\/mrow><\/msub><\/mrow>X_{i-1}<\/annotation><\/semantics><\/math><\/span>X<\/span>i<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3068\u3057\u307e\u3059\u3002\u3064\u307e\u308a\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u5b9a\u7fa9\u3067\u304d\u307e\u3059\u3002<\/p>\n

      <\/mstyle><\/mtd>(<\/mo>X<\/mi>i<\/mi>\u2212<\/mo>1<\/mn><\/mrow><\/msub>,<\/mo>s<\/mi>)<\/mo>=<\/mo>D<\/mi>(<\/mo>X<\/mi>i<\/mi><\/msub>)<\/mo><\/mrow><\/mstyle><\/mtd><\/mtr><\/mstyle><\/mtd>while\u00a0<\/mtext>X<\/mi>i<\/mi>\u2212<\/mo>1<\/mn><\/mrow><\/msub>k<\/mi>M<\/mi>:<\/mo><\/mo><\/mrow><\/mstyle><\/mtd><\/mtr><\/mstyle><\/mtd>\u2005\u200a<\/mtext>\u2005\u200a<\/mtext>\u2005\u200a<\/mtext>\u2005\u200a<\/mtext>X<\/mi>i<\/mi>\u2212<\/mo>1<\/mn><\/mrow><\/msub>\u2190<\/mo>X<\/mi>i<\/mi>\u2212<\/mo>1<\/mn><\/mrow><\/msub>\u22c5<\/mo>2<\/mn>n<\/mi><\/msup>+<\/mo>next\u00a0<\/mtext>k<\/mi><\/mstyle>\u00a0bits\u00a0from\u00a0bitstream<\/mtext><\/mrow><\/mrow><\/mstyle><\/mtd><\/mtr><\/mtable>\\begin{align}\n&(X_{i-1},s) = D(X_i)\\\\\n&\\text{while } X_{i-1} <\/annotation><\/semantics><\/math><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>X<\/span>i<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span>s<\/span>)<\/span>=<\/span>D<\/span>(<\/span>X<\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span>while\u00a0<\/span><\/span>X<\/span>i<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>k<\/span>M<\/span>:<\/span><\/span><\/span>X<\/span>i<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2190<\/span>X<\/span>i<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u22c5<\/span>2<\/span>n<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span>next\u00a0<\/span>k<\/span>\u00a0bits\u00a0from\u00a0bitstream<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

      \u3057\u304b\u3057\u3053\u3053\u3067\u3082\u3001\u7b26\u53f7\u5316\u4e2d\u306b\u884c\u308f\u308c\u308bk<\/mi><\/mrow>k<\/annotation><\/semantics><\/math><\/span>k<\/span><\/span><\/span><\/span>\u30d3\u30c3\u30c8\u306e\u8aad\u307f\u53d6\u308a\u306e\u56de\u6570\u304c\u5fa9\u53f7\u5316\u4e2d\u306e\u56de\u6570\u3068\u7570\u306a\u308a\u3001\u5fa9\u53f7\u5316\u304c\u5931\u6557\u3059\u308b\u306e\u3053\u3068\u304c\u3042\u308b\u306e\u3067\u306f\u306a\u3044\u304b\u3068\u7591\u554f\u306b\u601d\u3046\u304b\u3082\u3057\u308c\u307e\u305b\u3093\u3002<\/p>\n

      \u7279\u306b\u3001X<\/mi>i<\/mi><\/msub>\u2208<\/mo>I<\/mi><\/mrow>X_i \\in I<\/annotation><\/semantics><\/math><\/span>X<\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2208<\/span><\/span>I<\/span><\/span><\/span><\/span>\u3068\u306a\u3063\u305f\u3089k<\/mi><\/mrow>k<\/annotation><\/semantics><\/math><\/span>k<\/span><\/span><\/span><\/span>\u30d3\u30c3\u30c8\u306e\u8aad\u307f\u53d6\u308a\u3092\u505c\u6b62\u3057\u307e\u3059\u304c\u3001\u3053\u308c\u306f\u65e9\u3059\u304e\u308b\u3068\u3044\u3046\u3053\u3068\u306f\u8d77\u304d\u306a\u3044\u306e\u3067\u3057\u3087\u3046\u304b?\u3082\u3057\u304b\u3057\u305f\u3089\u30012<\/mn>k<\/mi><\/msup>X<\/mi>i<\/mi><\/msub>\u2208<\/mo>I<\/mi><\/mrow>2^kX_i\\in I<\/annotation><\/semantics><\/math><\/span>2<\/span>k<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>X<\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2208<\/span><\/span>I<\/span><\/span><\/span><\/span>\u3067\u3082\u3042\u308b\u53ef\u80fd\u6027\u306f\u306a\u3044\u3067\u3057\u3087\u3046\u304b?<\/p>\n

      \u5b9f\u306f\u3001\u3053\u308c\u3082I<\/mi><\/mrow>I<\/annotation><\/semantics><\/math><\/span>I<\/span><\/span><\/span><\/span>\u306e\u8a2d\u8a08\u306b\u3088\u308a\u3001X<\/mi><\/mrow>X<\/annotation><\/semantics><\/math><\/span>X<\/span><\/span><\/span><\/span>\u30682<\/mn>k<\/mi><\/msup>X<\/mi><\/mrow>2^k X<\/annotation><\/semantics><\/math><\/span>2<\/span>k<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>X<\/span><\/span><\/span><\/span>\u306e\u4e21\u65b9\u304cI<\/mi><\/mrow>I<\/annotation><\/semantics><\/math><\/span>I<\/span><\/span><\/span><\/span>\u306b\u542b\u307e\u308c\u308b\u3088\u3046\u306a\u6574\u6570X<\/mi><\/mrow>X<\/annotation><\/semantics><\/math><\/span>X<\/span><\/span><\/span><\/span>\u306f\u5b58\u5728\u3057\u306a\u3044\u3053\u3068\u304c\u4fdd\u8a3c\u3055\u308c\u3066\u3044\u307e\u3059\uff08\u3053\u306e\u4e8b\u5b9f\u306f\u4e0a\u8a18\u540c\u69d8\u7c21\u5358\u306b\u78ba\u304b\u3081\u3089\u308c\u308b\u306e\u3067\u3001\u6f14\u7fd2\u306b\u3054\u6d3b\u7528\u304f\u3060\u3055\u3044\uff01\uff09\u3002<\/p>\n

      \u3053\u308c\u306b\u3088\u308a\u3001\u30b9\u30c8\u30ea\u30fc\u30e0\u306e\u8aad\u307f\u53d6\u308a\u56de\u6570\u304c\u4e00\u610f\u306b\u6c7a\u5b9a\u3055\u308c\u308b\u3053\u3068\u304c\u4fdd\u8a3c\u3055\u308c\u3001\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u524d\u8ff0\u306e\u3088\u3046\u306a\u66d6\u6627\u306a\u72b6\u6cc1\u306b\u306f\u906d\u9047\u3057\u306a\u3044\u306e\u3067\u3059\u3002<\/p>\n

      \u4ee5\u4e0a\u3067\u3059\uff01\u3053\u308c\u3067\u5b9f\u7528\u7684\u306arANS\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u304c\u5b8c\u6210\u3057\u307e\u3057\u305f\u3002<\/p>\n

      \u6700\u5f8c\u306b\u3001\u975e\u5e38\u306b\u77ed\u304f\u3067\u306f\u3042\u308a\u307e\u3059\u304c\u3001tANS\u3068\u3044\u3046rANS\u3068\u975e\u5e38\u306b\u95a2\u4fc2\u306e\u6df1\u3044\u30a2\u30eb\u30b4\u30ea\u30b9\u30e0\u3092\u7d39\u4ecb\u3057\u307e\u3059\u3002<\/p>\n

      \u524d\u306e\u7bc0\u3067\u306f\u3001\u5404\u6642\u523bi<\/mi><\/mrow>i<\/annotation><\/semantics><\/math><\/span>i<\/span><\/span><\/span><\/span>\u306b\u304a\u3044\u3066\u72b6\u614b\u5024X<\/mi>i<\/mi><\/msub><\/mrow>X_i<\/annotation><\/semantics><\/math><\/span>X<\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3092\u7279\u5b9a\u306e\u7bc4\u56f2\u306b\u5236\u9650\u3059\u308brANS\u306e\u30b9\u30c8\u30ea\u30fc\u30df\u30f3\u30b0\u7248\u3092\u898b\u3066\u304d\u307e\u3057\u305f\u3002E<\/mi>(<\/mo>X<\/mi>,<\/mo>s<\/mi>)<\/mo><\/mrow>E(X,s)<\/annotation><\/semantics><\/math><\/span>E<\/span>(<\/span>X<\/span>,<\/span>s<\/span>)<\/span><\/span><\/span><\/span>\u306f\u4e00\u5bfe\u4e00\u306e\u5199\u50cf\uff08\u5358\u5c04\uff09\u3067\u3042\u308b\u305f\u3081\u3001rANS\u7b26\u53f7\u5316\u30d7\u30ed\u30bb\u30b9\u5168\u4f53\u3092\u901a\u3057\u3066E<\/mi>(<\/mo>X<\/mi>,<\/mo>s<\/mi>)<\/mo><\/mrow>E(X,s)<\/annotation><\/semantics><\/math><\/span>E<\/span>(<\/span>X<\/span>,<\/span>s<\/span>)<\/span><\/span><\/span><\/span>\u306b\u4f9b\u7d66\u3055\u308c\u308b\u5165\u529b\u306f\u6709\u9650\u500b\u3057\u304b\u3042\u308a\u307e\u305b\u3093\u3002<\/p>\n

      \u3088\u308a\u5177\u4f53\u7684\u306b\u306f\u3001\u30b9\u30c8\u30ea\u30fc\u30df\u30f3\u30b0rANS\u3067\u306f\u3001s<\/mi>\u2208<\/mo>S<\/mi><\/mrow>s \\in S<\/annotation><\/semantics><\/math><\/span>s<\/span>\u2208<\/span><\/span>S<\/span><\/span><\/span><\/span>\u3068X<\/mi>\u2208<\/mo>{<\/mo>l<\/mi>P<\/mi>(<\/mo>s<\/mi>)<\/mo>,<\/mo>\u22ef<\/mo>\u2009<\/mtext>,<\/mo>2<\/mn>k<\/mi><\/msup>l<\/mi>P<\/mi>(<\/mo>s<\/mi>)<\/mo>\u2212<\/mo>1<\/mn>}<\/mo><\/mrow>X \\in \\{lP(s),\\cdots,2^klP(s)-1\\}<\/annotation><\/semantics><\/math><\/span>X<\/span>\u2208<\/span><\/span>{<\/span>lP<\/span>(<\/span>s<\/span>)<\/span>,<\/span>\u22ef<\/span>,<\/span>2<\/span>k<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>lP<\/span>(<\/span>s<\/span>)<\/span>\u2212<\/span><\/span>1<\/span>}<\/span><\/span><\/span><\/span>\u306b\u5bfe\u3057\u3066E<\/mi>(<\/mo>X<\/mi>,<\/mo>s<\/mi>)<\/mo><\/mrow>E(X,s)<\/annotation><\/semantics><\/math><\/span>E<\/span>(<\/span>X<\/span>,<\/span>s<\/span>)<\/span><\/span><\/span><\/span>\u3092\u5b9a\u7fa9\u3059\u308c\u3070\u5341\u5206\u3067\u3042\u308a\u3001\u3053\u306e\u3088\u3046\u306a\u30da\u30a2(<\/mo>X<\/mi>,<\/mo>s<\/mi>)<\/mo><\/mrow>(X,s)<\/annotation><\/semantics><\/math><\/span>(<\/span>X<\/span>,<\/span>s<\/span>)<\/span><\/span><\/span><\/span>\u306f\u6709\u9650\u500b\u3057\u304b\u306a\u3044\u3068\u3044\u3046\u3053\u3068\u3067\u3059\u3002<\/p>\n

      tANS\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\uff08tabled Asymmetric Numerical System<\/strong>\uff09\u306f\u3001\u7b26\u53f7\u5316\/\u5fa9\u53f7\u5316\u30d7\u30ed\u30bb\u30b9\u306e\u958b\u59cb\u6642\u306bE<\/mi>(<\/mo>X<\/mi>,<\/mo>s<\/mi>)<\/mo><\/mrow>E(X,s)<\/annotation><\/semantics><\/math><\/span>E<\/span>(<\/span>X<\/span>,<\/span>s<\/span>)<\/span><\/span><\/span><\/span>\u306e\u8868\u3092\u4f5c\u6210\u3059\u308b\u3053\u3068\u3067rANS\u306e\u901f\u5ea6\u3092\u5411\u4e0a\u3055\u305b\u308b\u3001ANS\u65cf\u306e\u4e00\u7a2e\u3067\u3059\u3002\u3053\u306e\u8868\u306b\u3088\u308a\u3001\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u9664\u7b97\u3084\u6574\u6570\u4e57\u7b97\u3092\u542b\u3080E<\/mi>(<\/mo>X<\/mi>,<\/mo>s<\/mi>)<\/mo><\/mrow>E(X,s)<\/annotation><\/semantics><\/math><\/span>E<\/span>(<\/span>X<\/span>,<\/span>s<\/span>)<\/span><\/span><\/span><\/span>\u306e\u8a08\u7b97\u3092\u3001\u305f\u3060\u306e\u8868\u306e\u53c2\u7167\u306b\u307e\u3067\u524a\u6e1b\u3067\u304d\u307e\u3059\u3002<\/p>\n

      \u3053\u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u8ab2\u984c\u306f\u8868\u306e\u4f5c\u6210\u65b9\u6cd5\u306b\u3042\u308a\u307e\u3059\u3002E<\/mi>(<\/mo>X<\/mi>,<\/mo>s<\/mi>)<\/mo><\/mrow>E(X,s)<\/annotation><\/semantics><\/math><\/span>E<\/span>(<\/span>X<\/span>,<\/span>s<\/span>)<\/span><\/span><\/span><\/span>\u306e\u3059\u3079\u3066\u306e\u5024\u3092\u8a08\u7b97\u3059\u308b\u3053\u3068\u3082\u3067\u304d\u307e\u3059\u304c\u3001\u3053\u308c\u3067\u306fE<\/mi><\/mrow>E<\/annotation><\/semantics><\/math><\/span>E<\/span><\/span><\/span><\/span>\u306e\u8a08\u7b97\u3092\u907f\u3051\u308b\u3053\u3068\u3092\u76ee\u7684\u3068\u3059\u308btANS\u306e\u610f\u7fa9\u304c\u5931\u308f\u308c\u3066\u3057\u307e\u3044\u307e\u3059\u3002<\/p>\n

      Jarek Duda\u306e\u8ad6\u6587[1]\u306f\u3001\u3053\u308c\u3089\u306e\u8868\u306e\u5024\u3092\u660e\u793a\u7684\u306b\u8a08\u7b97\u3059\u308b\u3053\u3068\u306a\u304fE<\/mi>(<\/mo>X<\/mi>,<\/mo>s<\/mi>)<\/mo><\/mrow>E(X,s)<\/annotation><\/semantics><\/math><\/span>E<\/span>(<\/span>X<\/span>,<\/span>s<\/span>)<\/span><\/span><\/span><\/span>\u306e\u8868\u3092\u4f5c\u6210\u3059\u308b\u65b9\u6cd5\u3092\u793a\u3057\u3066\u3044\u307e\u3059\u304c\u3001\u305d\u306e\u65b9\u6cd5\u3092\u8a73\u3057\u304f\u8aac\u660e\u3057\u3066\u3044\u305f\u3089\u672c\u8a18\u4e8b\u306e\u7bc4\u56f2\u3092\u5927\u304d\u304f\u8d85\u3048\u3066\u3057\u307e\u3044\u307e\u3059\u306e\u3067\u3001\u4eca\u56de\u306f\u3053\u306e\u3042\u305f\u308a\u3067\u5fa1\u514d\u3092\u8499\u308a\u307e\u3059\u3002<\/p>\n

      \u672c\u8a18\u4e8b\u3067\u306f\u3001\u3042\u3089\u3086\u308b\u5727\u7e2e\u306e\u5834\u9762\u306b\u304a\u3044\u3066\u5f37\u529b\u306a\u30c4\u30fc\u30eb\u3068\u3057\u3066\u4f7f\u308f\u308c\u3066\u3044\u308brANS\u3068\u305d\u306e\u30b9\u30c8\u30ea\u30fc\u30df\u30f3\u30b0\u7248\u306b\u3064\u3044\u3066\u7d39\u4ecb\u3044\u305f\u3057\u307e\u3057\u305f\u3002<\/p>\n

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      \u307e\u305f\u3001\u5727\u7e2e\u7387\u3068\u8a08\u7b97\u8907\u96d1\u6027\u306e\u9593\u3067\u7570\u306a\u308b\u30c8\u30ec\u30fc\u30c9\u30aa\u30d5\u3092\u63d0\u4f9b\u3059\u308bANS\u65cf\u306e\u4e00\u7a2e\u3067\u3042\u308btANS\u306b\u3064\u3044\u3066\u3082\u7c21\u5358\u306b\u89e6\u308c\u307e\u3057\u305f\u3002<\/p>\n

      \u3053\u308c\u3089\u306e\u8fd1\u4ee3\u30a8\u30f3\u30c8\u30ed\u30d4\u30fc\u7b26\u53f7\u5316\u6280\u8853\u306f\u30013D\u30e2\u30c7\u30eb\u5727\u7e2e\u306e\u307f\u306a\u3089\u305a\u3001\u3055\u307e\u3056\u307e\u306a\u5834\u9762\u3067\u73fe\u4ee3\u306eIT\u6280\u8853\u3092\u5f71\u304b\u3089\u652f\u3048\u3066\u3044\u308b\u3001\u307e\u3055\u306b\u7e01\u306e\u4e0b\u306e\u529b\u6301\u3061\u3068\u8a00\u3063\u3066\u3088\u3044\u3068\u601d\u3044\u307e\u3059\u3002\u672c\u7a3f\u304c\u3001\u5c11\u3057\u3067\u3082\u591a\u304f\u306e\u65b9\u306b\u3068\u3063\u3066\u3001\u666e\u6bb5\u967d\u306e\u5f53\u305f\u3089\u306a\u3044\u5f7c\u3089\u3092\u77e5\u308b\u304d\u3063\u304b\u3051\u306b\u306a\u308c\u3070\u5e78\u3044\u3067\u3059\u3002<\/p>\n

      \u3067\u306f\u3001\u4eca\u56de\u306f\u3053\u308c\u306b\u3066\u3002<\/p>\n

        \n
      1. Duda, J. (2013). Asymmetric numeral systems: entropy coding combining speed of Huffman coding with compression rate of arithmetic coding. arXiv preprint arXiv:1311.2540<\/em>. https:\/\/arxiv.org\/pdf\/1311.2540<\/a><\/li>\n<\/ol>\n

        <\/span><\/div>\n\n
        \u5143\u306e\u8a18\u4e8b\u3092\u78ba\u8a8d\u3059\u308b <\/a><\/p>\n","protected":false},"excerpt":{"rendered":"\u3053\u3093\u306b\u3061\u306f\u3001Eukarya\u306e\u77e2\u6240\u3067\u3059\u3002 \u4eca\u56de\u306f3D\u30e2\u30c7\u30eb\u5727\u7e2e\u6280\u8853\u306b\u95a2\u3059\u308b\u9023\u8f09\u8a18\u4e8b\u306e\u7b2c2\u56de\u3068\u3057\u3066\u3001rANS\u306b\u3064\u3044\u3066\u53d6\u308a\u4e0a\u3052\u307e\u3059\u3002 ranged Asymmetric Numerical System \u3001\u7565\u3057\u3066rANS\u306f\u3001\u30a8 […]","protected":false},"author":1,"featured_media":24979,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[4],"tags":[],"class_list":["post-24978","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-company-tec"],"acf":[],"yoast_head":"\n3D\u30e2\u30c7\u30eb\u3092\u5727\u7e2e\u3059\u308b\u6280\u88532\uff1arANS\u3068\u306f | Re:Earth Engineering - 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