Counterexample challenges proposed relay channel capacity theory

Counterexample to a Proposed Capacity Characterization of the Relay Channel

Information Theory

Summary

This work shows that a recently suggested way to measure the maximum communication ability of a relay channel is incorrect. The relay channel connects a source to a destination with the help of a middle relay node. The authors found a simple example that gets better communication rates than the proposed theory allows. They used artificial intelligence to help find and simplify this example. This means the understanding of relay channels needs revision for general cases.

What this means in practice

  • For network engineers: Avoid relying on the disproven capacity formula when designing relay-based communication systems to prevent suboptimal performance estimations.
  • For wireless system designers: Use the new counterexample insights to guide the creation of more efficient relay communication protocols beyond previously accepted capacity limits.

A theory result. No direct application yet.

Authors

Chun Hei Michael Shiu

Abstract

We present a counterexample to the relay channel capacity characterization proposed in a recent work, which is based on properties of typical sequences. The counterexample uses a binary relay channel with a noiseless source-destination component and binary symmetric relay links. An achievable scheme exceeds the proposed capacity characterization, thereby disproving the characterization of the capacity for general relay channels. We highlight that the counterexample is obtained with the assistance of ChatGPT-6 Astra and the proofs are simplified with human effort.