A coding theorem for a class of stationary channels with feedback
A coding theorem for a class of stationary channels with feedback
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DOI：
10.1109/tit.2008.917685
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发表时间：
2008-04-01
影响因子：
2.5
通讯作者：
Kim, Young-Han
中科院分区：
文献类型：
--
作者：
Kim, Young-Han
证明了一类具有反馈的平稳信道的编码定理，其中输出为Y-n。= f (X-n-m(n) Z（n-m)(n)）是来自信道输入X的当前和过去的符号函数，以及平稳遍历信道噪声Z(n)。特别地，表明反馈容量等于[GRAPHICS]，其中I(x -n -> y -n) = Sigma(n)(I =1) I（x - I； y - I竖条Yi-1）表示从通道输入到输出的Massey有向信息，并且最高取自所有因果条件分布p(x(n)平行于y(n-1)) = Pi(n)(I =1) p(x(I)竖条x（I -1), y(I -1)）。证明的主要思想是香农策略在带边信息编码中的经典应用，以及一种新的无反馈信道模型的初等编码技术，该技术在某种意义上与Gallager的平稳遍历源的有损编码对偶。类似的方法给出了yang - kav&t atikonda、Chen-Berger和Permuter-Weissman-Goldsmith对有限状态信道编码定理的简单替代证明。
A coding theorem is proved for a class of stationary channels with feedback in which-the output Y-n. = f (X-n-m(n) Z(n-m)(n)) is the function of the current and past in symbols from the channel input X,, and the stationary ergodic channel noise Z(n). In particular, it is shown that the feedback capacity is equal to[GRAPHICS]where I(X-n -> Y-n) = Sigma(n)(i=1) I(X-i ; Y-i vertical bar Yi-1)denotes the Massey directed information from the channel input to the output, and the supremum is taken over all causally conditioned distributions p(x(n)parallel to y(n-1)) = Pi(n)(i=1) p(x(i)vertical bar x(i-1), y(i-1)). The main ideas of the proof are a classical application of the Shannon strategy for coding with side information and a new elementary coding technique for the given channel model without feedback, which is in a sense dual to Gallager's lossy coding of stationary ergodic sources. A similar approach gives a simple alternative proof of coding theorems for finite state channels by Yang-Kav&-Tatikonda, Chen-Berger, and Permuter-Weissman-Goldsmith.