Construction of Universal Channel Codes for Finite-State Channels

在移动通信中，关于信道的特性只能说一点。这促使许多研究人员研究编码和解码不依赖于特定信道的代码。这些代码通常被称为通用代码。从信息论的角度来看，通用码最早是由匈牙利研究人员cisszar、Korner和Matron于1977年提出的。他们证明了离散无记忆信道（DMC）的通用分组码的存在。不幸的是，DMC家族并不是一个现实的移动通信模型，因为它没有考虑由于衰落或码间干扰引起的信道记忆效应。为此，我们研究了最适合移动通信模型的有限状态信道族，得到了以下结果：(1)对于一类有限状态信道族，我们证明了存在编码和解码都不依赖于信道的通用分组码，并且所得到的通用码渐近地达到Gallager随机编码误差指数。(2)我们证明了通用信道解码器可以由任何通用源编码器构造。特别是对于接收方已知状态的DMS和FSC，我们给出了通用源代码可以用作通用信道解码器的充分条件。在此基础上，进一步证明了在采用通用解码器的情况下，存在一个码渐近地达到Gallager随机编码误差指数。

In mobile communications, only a little can be said about the characteristics of the channel. 'This prompted many researchers to investigate codes of which encoding and decoding do not depend on a particular channel. These codes are usually referred to as universal codes. From the viewpoint of information theory, universal codes were first proposed by the Hungarian researchers Csiszar, Korner and Matron in 1977. They proved the existence of universal block codes for discrete memoryless channels (DMC's). Unfortunately, a family of DMC's is not a realistic model for mobile communications since it does not consider memory effect of the channel due to fading or intersymbol interferences. For this purpose, we have investigate a family of finite state channels (FSC's) which is the most appropriate candidate for the model of mobile communication, and obtained the following results:(1) For a family of FSC's, we prove that there exist universal block codes of which both encoding and decoding do not depend on the channel, and that the obtained universal codes asymptotically achieves Gallager's random coding error exponent.(2) We show that universal channel decoder can be constructed from any universal source encoder. Especially, for the class of DMS's and FSC's where the state is known to the receiver, we show the sufficient conditions that the universal source code can be utilized as the universal channel decoder. Further, we show that there exists a code which asymptotically achieves Gallager's random coding error exponent when the proposed universal decoder is employed.