Mismatched Multi-Letter Successive Decoding for the Multiple-Access Channel

TL;DR

This paper introduces a multi-letter successive decoding approach for the discrete memoryless multiple-access channel, demonstrating improved achievable rate regions and error exponents, especially in cognitive scenarios, compared to traditional decoding methods.

Contribution

It develops a novel multi-letter successive decoding rule based on arbitrary metrics, providing tighter rate regions and error exponents for both standard and cognitive MACs.

Findings

Successive decoding can achieve higher sum rates than traditional methods.

Derived achievable rate regions and error exponents for both MAC types.

Numerical examples show the advantage of successive decoding in certain cases.

Abstract

This paper studies channel coding for the discrete memoryless multiple-access channel with a given (possibly suboptimal) decoding rule. A multi-letter successive decoding rule depending on an arbitrary non-negative decoding metric is considered, and achievable rate regions and error exponents are derived both for the standard MAC (independent codebooks), and for the cognitive MAC (one user knows both messages) with superposition coding. In the cognitive case, the rate region and error exponent are shown to be tight with respect to the ensemble average. The rate regions are compared with those of the commonly-considered decoder that chooses the message pair maximizing the decoding metric, and numerical examples are given for which successive decoding yields a strictly higher sum rate for a given pair of input distributions.