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首页> 外文期刊>IEEE Transactions on Information Theory >A Coding Theorem for a Class of Stationary Channels With Feedback
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A Coding Theorem for a Class of Stationary Channels With Feedback

机译：一类带反馈固定信道的编码定理

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摘要

A coding theorem is proved for a class of stationary channels with feedback in which the output $Y_{n} = fleft(X_{n-m}^{n}, Z_{n-m}^{n}right)$ is the function of the current and past $m$ symbols from the channel input $X_{n}$ and the stationary ergodic channel noise $Z_{n}$ . In particular, it is shown that the feedback capacity is equal to $$lim_{nto infty } sup_{p(x^{n}Vert y^{n-1})}{{ 1}over { n}} I(X^{n} to Y^{n})$$ where $I(X^{n} to Y^{n}) = sum _{i=1}^{n} Ileft(X^{i}; Y_{i}vert Y^{i-1}right)$ denotes the Massey directed information from the channel input to the output, and the supremum is taken over all causally conditioned distributions $p(x^{n}Vert y^{n-1}) = prod _{i=1}^{n} pleft(x_{i}vert x^{i-1},y^{i-1}right)$. 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–KavČiĆ–Tatikonda, Chen–Berger, and Permuter–Weissman–Goldsmith.
机译：证明了针对一类具有反馈的平稳信道的编码定理，其中输出$ Y_ {n} = fleft（X_ {nm} ^ {n}，Z_ {nm} ^ {n} right）$是函数的函数。通道输入$ X_ {n} $的当前和过去$ m $符号以及平稳的遍历通道噪声$ Z_ {n} $。特别地，表明反馈容量等于{lim} {I}上的$$ lim_ {nto infty} sup_ {p（x ^ {n} Vert y ^ {n-1}）} {{1} X ^ {n}至Y ^ {n}）$$其中$ I（X ^ {n}至Y ^ {n}）=和_ {i = 1} ^ {n} Ileft（X ^ {i}; Y_ {i} vert Y ^ {i-1} right）$表示从通道输入到输出的梅西有向信息，并且对所有因果条件分布$ p（x ^ {n} Vert y ^ { n-1}）=产品_ {i = 1} ^ {n} pleft（x_ {i} vert x ^ {i-1}，y ^ {i-1} right）$。证明的主要思想是香农策略用于边信息编码的经典应用，以及给定信道模型在没有反馈的情况下的新基本编码技术，这在某种意义上是固定的Gallager的有损编码的对偶遍历来源。一种类似的方法由Yang–KavČiĆ–Tatikonda，Chen–Berger和Permuter–Weissman–Goldsmith为有限状态通道的编码定理提供了简单的替代证明。

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