Achievable rate region based on coset codes for multiple access channel with states

TL;DR

This paper introduces a new algebraic coding framework using coset codes for multiple access channels with states, achieving larger rate regions than traditional methods by exploiting algebraic structures.

Contribution

It develops a novel coding technique based on nested coset codes for channels with states, expanding the achievable rate region beyond existing unstructured code approaches.

Findings

Achieves capacity for discrete memoryless point-to-point channels using nested coset codes.

Derives a new achievable rate region for multiple access channels with states.

Identifies scenarios where the proposed codes outperform random unstructured codes.

Abstract

We prove that the ensemble the nested coset codes built on finite fields achieves the capacity of arbitrary discrete memoryless point-to-point channels. Exploiting it's algebraic structure, we develop a coding technique for communication over general discrete multiple access channel with channel state information distributed at the transmitters. We build an algebraic coding framework for this problem using the ensemble of Abelian group codes and thereby derive a new achievable rate region. We identify non-additive and non-symmteric examples for which the proposed achievable rate region is strictly larger than the one achievable using random unstructured codes.