Construction of Multiple Access Channel Codes Based on Hash Property

TL;DR

This paper proposes a new method for constructing codes for discrete stationary memoryless multiple access channels using hash properties of sparse matrices, potentially enabling efficient approximation algorithms.

Contribution

It introduces a novel code construction approach based on hash properties and sparse matrices for multiple access channels, differing from traditional random coding methods.

Findings

Sparse matrices possess a hash property suitable for code construction

The proposed method may enable efficient approximation algorithms

Potential advantages over conventional random coding approaches

Abstract

The aim of this paper is to introduce the construction of codes for a general discrete stationary memoryless multiple access channel based on the the notion of the hash property. Since an ensemble of sparse matrices has a hash property, we can use sparse matrices for code construction. Our approach has a potential advantage compared to the conventional random coding because it is expected that we can use some approximation algorithms by using the sparse structure of codes.