On the Non-Adaptive Zero-Error Capacity of the Discrete Memoryless Two-Way Channel

TL;DR

This paper investigates the zero-error communication capacity of discrete memoryless two-way channels using non-adaptive schemes, deriving bounds and exploring the role of graph spectra to improve understanding of capacity limits.

Contribution

It introduces new single-letter bounds for the zero-error capacity region of two-way channels, combining classical and novel techniques, including graph spectra analysis.

Findings

Single-letter outer bound improves upon previous bounds.

The asymptotic spectrum of graphs can achieve certain capacity bounds.

New bounds are tighter for specific two-way channel cases.

Abstract

We study the problem of communicating over a discrete memoryless two-way channel using non-adaptive schemes, under a zero probability of error criterion. We derive single-letter inner and outer bounds for the zero-error capacity region, based on random coding, linear programming, linear codes, and the asymptotic spectrum of graphs. Among others, we provide a single-letter outer bound based on a combination of Shannon's vanishing-error capacity region and a two-way analogue of the linear programming bound for point-to-point channels, which in contrast to the one-way case, is generally better than both. Moreover, we establish an outer bound for the zero-error capacity region of a two-way channel via the asymptotic spectrum of graphs and show that this bound could be achieved for certain cases.