Universal decoding for channels with memory

A universal decoder for a parametric family of channels is a decoder whose structure depends on the family but not on the individual channel over which transmission takes place, and it yet attains the same random-coding error exponent as the maximum-likelihood receiver tuned to the channel in use. The existence and structure of such decoders is demonstrated under relatively mild conditions of continuity of the channel law with respect to the parameter indexing the family. It is further shown that under somewhat stronger conditions on the family of channels, the convergence of the performance of the universal decoder to that of the optimal decoder is uniform over the set of channels. Examples of families for which universal decoding is demonstrated include the family of finite-state channels and the family of Gaussian intersymbol interference channels.