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首页> 外文期刊>IEEE Transactions on Information Theory >Error Exponents for Recursive Decoding of Reed–Muller Codes on a Binary-Symmetric Channel
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Error Exponents for Recursive Decoding of Reed–Muller Codes on a Binary-Symmetric Channel

机译：二进制对称信道上的Reed-Muller码递归解码的误差指数

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摘要

Error exponents are studied for recursive decoding of Reed-Muller (RM) codes and their subcodes used on a binary-symmetric channel. The decoding process is first decomposed into similar steps, with one new information bit derived in each step. Multiple recursive additions and multiplications of the randomly corrupted channel outputs plusmn1 are performed using a specific order of these two operations in each step. Recalculated random outputs are compared in terms of their exponential moments. As a result, tight analytical bounds are obtained for decoding error probability of the two recursive algorithms considered in the paper. For both algorithms, the derived error exponents almost coincide with simulation results. Comparison of these bounds with similar bounds for bounded distance decoding and majority decoding shows that recursive decoding can reduce the output error probability of the latter two algorithms by five or more orders of magnitude even on the short block length of 256. It is also proven that the error probability of recursive decoding can be exponentially reduced by eliminating one or a few information bits from the original RM code
机译：研究了误差指数，以对二进制对称信道上使用的Reed-Muller（RM）码及其子码进行递归解码。首先将解码过程分解为相似的步骤，并在每个步骤中导出一个新的信息位。在每个步骤中，使用这两个操作的特定顺序执行随机破坏的通道输出plusmn1的多次递归加法和乘法。重新计算的随机输出将根据其指数矩进行比较。结果，获得了针对本文所考虑的两种递归算法的解码错误概率的严格解析边界。对于这两种算法，得出的误差指数几乎与仿真结果一致。将这些边界与有界距离解码和多数解码的相似边界进行比较表明，即使在256的短块长度上，递归解码也可以将后两种算法的输出错误概率降低5个或更多个数量级。通过从原始RM代码中消除一个或几个信息位，可以以指数方式降低递归解码的错误概率

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