On capacities of the two-user union channel with complete feedback

TL;DR

This paper determines the exact symmetric capacity for a two-user union channel with complete feedback for input alphabet sizes 3, 4, and 5, completing previous results for sizes 2 and at least 6.

Contribution

It extends the capacity characterization of the two-user union channel with feedback to intermediate alphabet sizes and introduces a near-optimal coding scheme for zero-error communication.

Findings

Exact symmetric capacity for alphabet sizes 3, 4, 5 determined.

A practical near-optimal coding scheme for zero-error capacity provided.

Improves upon all previous explicit constructions.

Abstract

The exact values of the optimal symmetric rate point in the Cover--Leung capacity region of the two-user union channel with complete feedback were determined by Willems when the size of the input alphabet is 2, and by Vinck, Hoeks and Post when the size is at least 6. We complete this line of research when the size of the input alphabet is 3, 4 or 5. The proof hinges on the technical lemma that concerns the maximal joint entropy of two independent random variables in terms of their probability of equality. For the zero-error capacity region, using superposition coding, we provide a practical near-optimal communication scheme which improves all the previous explicit constructions.