信源信道联合编码的信息谱方法
An information-spectrum approach to joint source-channel coding
摘要：
给定具有{ \em可数无限}信源字母表的一般信源$\sV=\{V^n\}\noi$和具有任意{ \em abstract}信道输入输出字母表的一般信道$\sW=\{W^n\}\noi$，从信息谱的角度研究信源信道联合编码问题.首先，我们推广了Feinstein引理（直接部分）和Verdú-Han引理（逆部分），使其适用于一般的联合信源信道编码问题。基于这些引理，我们建立了信源$\sV$在信道$\sW$上可靠传输且误差概率渐近为零的充分条件和必要条件.结果表明，我们的充分条件与Vembu，Verdú和Steinberg的充分条件一致，而我们的必要条件比他们的必要条件强得多.实际上，如果我们忽略这些条件中出现的一些渐近为零的项，我们的必要条件与我们的充分条件是一致的。此外，它表明，{ \em分离定理}在广义上总是成立。此外，我们还证明了$\vep$ -可传性（$0\le \vep <1$）的一个充分条件和一个必要条件.最后，证明了传统标准式的分离定理对于满足（半）强逆性质的信源和信道类是成立的。
英文摘要：
Given a general source $\sV=\{V^n\}\noi$ with {\em countably infinite} source alphabet and a general channel $\sW=\{W^n\}\noi$ with arbitrary {\em abstract} channel input and output alphabets, we study the joint source-channel coding problem from the information-spectrum point of view. First, we generalize Feinstein's lemma (direct part) and Verdú-Han's lemma (converse part) so as to be applicable to the general joint source-channel coding problem. Based on these lemmas, we establish a sufficient condition as well as a necessary condition for the source $\sV$ to be reliably transmissible over the channel $\sW$ with asymptotically vanishing probability of error. It is shown that our sufficient condition coincides with the sufficient condition derived by Vembu, Verdú and Steinberg, whereas our necessary condition is much stronger than the necessary condition derived by them. Actually, our necessary condition coincide with our sufficient condition if we disregard some asymptotically vanishing terms appearing in those conditions. Also, it is shown that {\em Separation Theorem} in the generalized sense always holds. In addition, we demonstrate a sufficient condition as well as a necessary condition for the $\vep$-transmissibility ($0\le \vep <1$). Finally, the separation theorem of the traditional standard form is shown to hold for the class of sources and channels that satisfy the (semi-) strong converse property.
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。
