Computing sum of sources over an arbitrary multiple access channel

TL;DR

This paper introduces a new coding technique using nested coset codes for computing the sum of sources over arbitrary multiple access channels, outperforming previous methods like linear computation coding in various scenarios.

Contribution

It develops a novel set of sufficient conditions for source sum computation over any MAC using nested coset codes, extending beyond linear channels and integrating separation strategies.

Findings

Outperforms linear computation coding on non-linear MACs

Provides new sufficient conditions for sum computation over arbitrary MACs

Enhances techniques by combining nested coset codes with separation strategies

Abstract

The problem of computing sum of sources over a multiple access channel (MAC) is considered. Building on the technique of linear computation coding (LCC) proposed by Nazer and Gastpar [2007], we employ the ensemble of nested coset codes to derive a new set of sufficient conditions for computing the sum of sources over an \textit{arbitrary} MAC. The optimality of nested coset codes [Padakandla, Pradhan 2011] enables this technique outperform LCC even for linear MAC with a structural match. Examples of nonadditive MAC for which the technique proposed herein outperforms separation and systematic based computation are also presented. Finally, this technique is enhanced by incorporating separation based strategy, leading to a new set of sufficient conditions for computing the sum over a MAC.