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首页> 外文期刊>IEEE Transactions on Information Theory >Error Exponents of Erasure/List Decoding Revisited Via Moments of Distance Enumerators
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Error Exponents of Erasure/List Decoding Revisited Via Moments of Distance Enumerators

机译：通过距离枚举器的矩重新讨论擦除/列表解码的错误指数

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摘要

The analysis of random coding error exponents pertaining to erasure/list decoding, due to Forney, is revisited. Instead of using Jensen's inequality as well as some other inequalities in the derivation, we demonstrate that an exponentially tight analysis can be carried out by assessing the relevant moments of certain distance enumerators. The resulting bound has the following advantages: (i) it is at least as tight as Forney's bound, (ii) under certain symmetry conditions associated with the channel and the random coding distribution, it is simpler than Forney's bound in the sense that it involves an optimization over one parameter only (rather than two), and (iii) in certain special cases, like the binary symmetric channel (BSC), the optimum value of this parameter can be found in closed form, and so, there is no need to conduct a numerical search. We have not found yet a numerical example where this new bound is strictly better than Forney's bound and this may provide an additional evidence to support Forney's conjecture that his bound is tight for the average code. However, when applying the proposed analysis technique to a certain universal decoder with erasures, we demonstrate that it may yield significantly tighter exponential error bounds. We believe that this technique can be useful in simplifying and improving exponential error bounds in other problem settings as well.
机译：重新讨论了与Forney相关的与擦除/列表解码有关的随机编码错误指数的分析。我们没有在推导中使用詹森不等式和其他一些不等式，而是证明可以通过评估某些距离枚举器的相关矩来进行指数紧分析。生成的边界具有以下优点：（i）它至少与Forney边界一样紧密；（ii）在与通道和随机编码分布相关的某些对称条件下，从某种意义上说，它比Forney边界更简单仅对一个参数（而不是两个）进行优化，并且（iii）在某些特殊情况下，例如二进制对称信道（BSC），可以以封闭形式找到该参数的最佳值，因此，不需要进行数值搜索。我们还没有找到一个数值示例，该新界限严格比Forney界限更好，这可能提供了额外的证据来支持Forney的猜想，即他的界限对于平均代码而言是紧密的。但是，将拟议的分析技术应用于带有擦除的某些通用解码器时，我们证明了它可能会产生更紧密的指数误差范围。我们认为，该技术在简化和改善其他问题设置中的指数误差范围方面也很有用。

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