On Multiple Decoding Attempts for Reed–Solomon Codes: A Rate-Distortion Approach
On Multiple Decoding Attempts for Reed–Solomon Codes: A Rate-Distortion Approach
复制标题
关于里德所罗门码的多次解码尝试：率失真方法
DOI：
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发表时间：
2010
影响因子：
2.5
通讯作者：
K. Narayanan
中科院分区：
文献类型：
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作者：
Phong S. Nguyen;H. Pfister;K. Narayanan
里德-所罗门 (RS) 码软决策解码的一种流行方法是基于使用简单 RS 解码算法的多次试验，并在每次试验中擦除或翻转一组符号或位。本文提出了一个基于率失真（RD）理论的框架来分析这些多重解码算法。通过在错误模式和擦除模式之间定义适当的失真测量，对于单个错误和擦除解码尝试的成功解码条件变得等同于失真小于固定阈值。寻找最好的擦除模式集也变成了一个可以通过 RD 理论渐近解决的覆盖问题。因此，所提出的方法可用于理解 RS 码的多个错误和擦除解码的渐近性能与复杂性权衡。这个初步结果也被扩展了几个方向。计算率失真指数 (RDE) 可以为中等块长度提供更精确的结果。使用该框架分析了代数软决策（ASD）解码的多次试验。还介绍了 RD 和 RDE 函数的分析和数值计算。最后，仿真结果表明，使用所提出的方法设计的擦除模式集在相同数量的解码试验中优于其他算法。
One popular approach to soft-decision decoding of Reed-Solomon (RS) codes is based on using multiple trials of a simple RS decoding algorithm in combination with erasing or flipping a set of symbols or bits in each trial. This paper presents a framework based on rate-distortion (RD) theory to analyze these multiple-decoding algorithms. By defining an appropriate distortion measure between an error pattern and an erasure pattern, the successful decoding condition, for a single errors-and-erasures decoding trial, becomes equivalent to distortion being less than a fixed threshold. Finding the best set of erasure patterns also turns into a covering problem that can be solved asymptotically by RD theory. Thus, the proposed approach can be used to understand the asymptotic performance-versus-complexity tradeoff of multiple errors-and-erasures decoding of RS codes. This initial result is also extended a few directions. The rate-distortion exponent (RDE) is computed to give more precise results for moderate blocklengths. Multiple trials of algebraic soft-decision (ASD) decoding are analyzed using this framework. Analytical and numerical computations of the RD and RDE functions are also presented. Finally, simulation results show that sets of erasure patterns designed using the proposed methods outperform other algorithms with the same number of decoding trials.