The typical behaviour of relays

TL;DR

This paper analyzes the typical behavior of relay channels and relay arrays under LDPC coding using statistical mechanics, providing exact analytical results at Nishimori's temperature and quantifying performance improvements.

Contribution

It introduces an analytical solution for demodulate-and-forward strategy in relay channels using the replica symmetric ansatz, applicable at Nishimori's temperature.

Findings

Quantifies performance improvement with relay units

Provides exact analytical results at Nishimori's temperature

Analyzes small and large relay array configurations

Abstract

The typical behaviour of the relay-without-delay channel and its many-units generalisation, termed the relay array, under LDPC coding, is studied using methods of statistical mechanics. A demodulate-and-forward strategy is analytically solved using the replica symmetric ansatz which is exact in the studied system at the Nishimori's temperature. In particular, the typical level of improvement in communication performance by relaying messages is shown in the case of small and large number of relay units.