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arXiv 2007.15664cs.ITmath.IT
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多址信道的扭相关二阶逆界

A Second-Order Converse Bound for the Multiple-Access Channel via Wringing Dependence

Oliver Kosut

摘要:

在平均差错概率约束下,给出了两用户多址信道的一个新的逆界。该界限表明,对于大多数感兴趣的信道,二阶编码率(即,最佳可实现速率与渐近容量区域之间的差作为具有固定错误概率的块长度$n$的函数)是每个信道使用的$O(1/\sqrt{n})$比特。这个逆证明背后的主要工具是一个新的衡量两个随机变量之间的依赖性称为拧干依赖性,因为它的灵感来自Ahlswede的拧干技术。的$O(1/\sqrt{n})$间隙示出为任何信道满足一定的规律性条件,其中包括所有离散无记忆信道和高斯多址接入信道。精确的上限作为一个函数的错误的概率被证明的系数在$O(1/\sqrt{n})$长期,虽然对于大多数渠道,他们不匹配现有的可实现的界限。

英文摘要:

A new converse bound is presented for the two-user multiple-access channel under the average probability of error constraint. This bound shows that for most channels of interest, the second-order coding rate -- that is, the difference between the best achievable rates and the asymptotic capacity region as a function of blocklength $n$ with fixed probability of error -- is $O(1/\sqrt{n})$ bits per channel use. The principal tool behind this converse proof is a new measure of dependence between two random variables called wringing dependence, as it is inspired by Ahlswede's wringing technique. The $O(1/\sqrt{n})$ gap is shown to hold for any channel satisfying certain regularity conditions, which includes all discrete-memoryless channels and the Gaussian multiple-access channel. Exact upper bounds as a function of the probability of error are proved for the coefficient in the $O(1/\sqrt{n})$ term, although for most channels they do not match existing achievable bounds.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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