Construction of Universal Channel Codes for Finite-State Channels

在移动的通信中，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。从信息论的观点出发，普适码首先由匈牙利研究人员Csiszar、Korner和Matron于1977年提出。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，一个家庭的DMC的是不是一个现实的模型，移动的通信，因为它不考虑记忆效应的信道由于衰落或符号间干扰。为此，我们研究了一类最适合于移动的通信模型的有限状态信道（FSC），得到了如下结果：（1）对于一类FSC，我们证明了存在编码和译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)我们表明，通用信道解码器可以从任何通用的源编码器。特别是，对于类DMS的和FSC的状态是已知的接收器，我们显示的充分条件，通用的源代码可以被用作通用的信道解码器。此外，我们表明，存在一个代码，渐近达到Gallager的随机编码误差指数时，建议的通用解码器。

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.