A New Sphere-Packing Bound for Maximal Error Exponent for Multiple-Access Channels

TL;DR

This paper introduces a novel sphere-packing bound for the maximal error exponent in two-user discrete memoryless multiple-access channels, explicitly considering user input independence to achieve tighter bounds than previous results.

Contribution

It presents the first sphere-packing bound that explicitly enforces user input independence, leading to a more accurate maximal error exponent for DM MACs.

Findings

Tighter sphere-packing exponent than previous bounds

Explicitly accounts for user input independence

Improves understanding of error probabilities in MACs

Abstract

In this work, a new lower bound for the maximal error probability of a two-user discrete memoryless (DM) multiple-access channel (MAC) is derived. This is the first bound of this type that explicitly imposes independence of the users' input distributions (conditioned on the time-sharing auxiliary variable) and thus results in a tighter sphere-packing exponent when compared to the tightest known exponent derived by Haroutunian.