Random coding bounds that attain the joint source-channel exponent

This paper presents a random-coding upper bound on the average error probability of joint source-channel coding that attains Csiszár´s error exponent. The bound is based on a code construction for which source messages are assigned to disjoint subsets (classes), and codewords are generated according to a distribution that depends on the class of the source message. For a single class, the bound recovers Gallager´s exponent; identifying the classes with source type classes, it recovers Csiszár´s exponent. Moreover, it is shown that as a two appropriately designed classes are sufficient to attain Csiszár´s exponent.