A Tight Upper Bound on the Second-Order Coding Rate of the Parallel Gaussian Channel With Feedback
A Tight Upper Bound on the Second-Order Coding Rate of the Parallel Gaussian Channel With Feedback
复制标题
带反馈的并行高斯信道二阶编码率的严格上限
DOI：
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发表时间：
2017
影响因子：
2.5
通讯作者：
V. Tan
中科院分区：
文献类型：
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作者：
S. Fong;V. Tan
本文研究了在以下设置下带反馈的并行高斯信道上固定长度码最大速率的渐近展开：对每个传输码字施加峰值功率约束，并且随着块长度的增加，解码传输消息的平均错误概率不为零。本文的主要贡献是带反馈的并行高斯通道的一阶和二阶渐近上限的独立证明。证明技术涉及开发信息谱界限，然后使用柯蒂斯定理来证明与信息谱界限相关的相关随机变量之和在分布中收敛于独立随机变量之和，从而便于使用通常的中心极限定理。结合现有的可实现性结果，我们的结果表明反馈的存在不会改善一阶和二阶渐近。
This paper investigates the asymptotic expansion for the maximum rate of fixed-length codes over a parallel Gaussian channel with feedback under the following setting: a peak power constraint is imposed on every transmitted codeword, and the average error probabilities of decoding the transmitted message are non-vanishing as the blocklength increases. The main contribution of this paper is a self-contained proof of an upper bound on the first- and second-order asymptotics of the parallel Gaussian channel with feedback. The proof techniques involve developing an information spectrum bound followed by using Curtiss’ theorem to show that a sum of dependent random variables associated with the information spectrum bound converges in distribution to a sum of independent random variables, thus facilitating the use of the usual central limit theorem. Combined with existing achievability results, our result implies that the presence of feedback does not improve the first- and second-order asymptotics.