Near-Optimal Coding for Many-user Multiple Access Channels

TL;DR

This paper introduces near-optimal coding schemes for many-user Gaussian multiple access channels, analyzing tradeoffs between energy, user density, and spectral efficiency using AMP decoding and spatial coupling.

Contribution

It proposes efficient coding schemes based on random linear models with AMP decoding that achieve near-optimal performance in large systems.

Findings

Spatially coupled coding with AMP achieves near-optimal tradeoffs.

Tradeoff analysis between energy-per-bit and user density.

Methods to reduce decoding complexity for large payloads.

Abstract

This paper considers the Gaussian multiple-access channel (MAC) in the asymptotic regime where the number of users grows linearly with the code length. We propose efficient coding schemes based on random linear models with approximate message passing (AMP) decoding and derive the asymptotic error rate achieved for a given user density, user payload (in bits), and user energy. The tradeoff between energy-per-bit and achievable user density (for a fixed user payload and target error rate) is studied, and it is demonstrated that in the large system limit, a spatially coupled coding scheme with AMP decoding achieves near-optimal tradeoffs for a wide range of user densities. Furthermore, in the regime where the user payload is large, we also study the tradeoff between energy-per-bit and spectral efficiency and discuss methods to reduce decoding complexity.