Universal decoding for arbitrary channels relative to a given class of decoding metrics

TL;DR

This paper introduces a universal decoding method for arbitrary unknown channels that performs nearly as well as the best decoder in a given class, applicable to mismatched, universal, and deterministic channels, with extensions to feedback and multiple access scenarios.

Contribution

It proposes a generic universal decoder that guarantees near-optimal error performance within a class of decoders for arbitrary channels, unifying several decoding paradigms.

Findings

Universal decoder's error probability is within a sub-exponential factor of the best decoder.

The approach generalizes previous results on universal decoding as special cases.

Method extends to scenarios with feedback and multiple access channels.

Abstract

We consider the problem of universal decoding for arbitrary unknown channels in the random coding regime. For a given random coding distribution and a given class of metric decoders, we propose a generic universal decoder whose average error probability is, within a sub-exponential multiplicative factor, no larger than that of the best decoder within this class of decoders. Since the optimum, maximum likelihood (ML) decoder of the underlying channel is not necessarily assumed to belong to the given class of decoders, this setting suggests a common generalized framework for: (i) mismatched decoding, (ii) universal decoding for a given family of channels, and (iii) universal coding and decoding for deterministic channels using the individual-sequence approach. The proof of our universality result is fairly simple, and it is demonstrated how some earlier results on universal decoding are obtained as special cases. We also demonstrate how our method extends to more complicated scenarios, like incorporation of noiseless feedback, and the multiple access channel.