A New Upper Bound on the Average Error Exponent for Multiple-Access Channels

TL;DR

This paper introduces a tighter lower bound on the average error probability for two-user discrete memoryless multiple-access channels, improving upon existing bounds by explicitly considering user input independence.

Contribution

It derives a new sphere packing bound that explicitly accounts for user input independence, resulting in a tighter error exponent for MACs.

Findings

Tighter sphere packing bound for average error probability

Explicitly accounts for user input independence

Relates average and maximal error probabilities

Abstract

A new lower bound for the average probability or error for a two-user discrete memoryless (DM) multiple-access channel (MAC) is derived. This bound has a structure very similar to the well-known sphere packing packing bound derived by Haroutunian. However, since explicitly imposes independence of the users' input distributions (conditioned on the time-sharing auxiliary variable) results in a tighter sphere-packing exponent in comparison to Haroutunian's. Also, the relationship between average and maximal error probabilities is studied. Finally, by using a known sphere packing bound on the maximal probability of error, a lower bound on the average error probability is derived.