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首页> 外文期刊>IEEE Transactions on Information Theory >Bit-error probability for maximum-likelihood decoding of linear block codes and related soft-decision decoding methods
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Bit-error probability for maximum-likelihood decoding of linear block codes and related soft-decision decoding methods

机译：线性块码最大似然解码的误码概率及相关的软判决解码方法

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摘要

In this correspondence, the bit-error probability P/sub b/ for maximum-likelihood decoding of binary linear block codes is investigated. The contribution P/sub b/(j) of each information bit j to P/sub b/ is considered and an upper bound on P/sub b/(j) is derived. For randomly generated codes, it is shown that the conventional approximation at high SNR P/sub b//spl ap/(d/sub H//N).P/sub s/, where P/sub s/ represents the block error probability, holds for systematic encoding only. Also systematic encoding provides the minimum P/sub b/ when the inverse mapping corresponding to the generator matrix of the code is used to retrieve the information sequence. The bit-error performances corresponding to other generator matrix forms are also evaluated. Although derived for codes with a generator matrix randomly generated, these results are shown to provide good approximations for codes used in practice. Finally, for soft-decision decoding methods which require a generator matrix with a particular structure such as trellis decoding, multistage decoding, or algebraic-based soft-decision decoding, equivalent schemes that reduce the bit-error probability are discussed. Although the gains achieved at practical bit-error rates are only a fraction of a decibel, they remain meaningful as they are of the same orders as the error performance differences between optimum and suboptimum decodings. Most importantly, these gains are free as they are achieved with no or little additional circuitry which is transparent to the conventional implementation.
机译：在这种对应关系中，研究了用于二进制线性块码的最大似然解码的误码概率P / sub b /。考虑每个信息比特j对P / sub b /的贡献P / sub b /（j），并得出P / sub b /（j）的上限。对于随机生成的代码，表明在高SNR P / sub b // spl ap /（d / sub H // N）.P / sub s /时的常规逼近，其中P / sub s /代表块误差概率，仅适用于系统编码。当与代码的生成器矩阵相对应的逆映射用于检索信息序列时，系统编码也提供最小P / sub b /。还评估了与其他生成器矩阵形式相对应的误码性能。尽管从具有随机生成的生成器矩阵的代码导出，但这些结果显示出可以为实际使用的代码提供良好的近似值。最后，对于需要具有特定结构的生成器矩阵的软决策解码方法（例如网格解码，多级解码或基于代数的软决策解码），讨论了降低误码率的等效方案。尽管在实际的误码率下获得的增益仅为分贝的一小部分，但它们仍然有意义，因为它们与最佳和次最佳解码之间的差错性能差异相同。最重要的是，这些增益是免费的，因为它们不需要或几乎没有对常规实现透明的附加电路来实现。

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