Construction of Universal Channel Codes for Finite-State Channels

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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.