Statistical Mechanics of Broadcast Channels Using Low Density Parity Check Codes

TL;DR

This paper analyzes the performance of LDPC codes in broadcast channels using statistical physics methods, demonstrating that belief propagation improves practical performance over timesharing, but optimal decoding is limited by the timesharing bound.

Contribution

It applies statistical physics analysis to LDPC codes in broadcast channels, revealing the performance limits of belief propagation and optimal decoding.

Findings

Belief propagation outperforms timesharing in practical scenarios.

Optimal decoding performance is bounded by the timesharing limit.

LDPC codes with linear combinations outperform simple timesharing methods.

Abstract

We investigate the use of Gallager's low-density parity-check (LDPC) codes in a broadcast channel, one of the fundamental models in network information theory. Combining linear codes is a standard technique in practical network communication schemes and is known to provide better performance than simple timesharing methods when algebraic codes are used. The statistical physics based analysis shows that the practical performance of the suggested method, achieved by employing the belief propagation algorithm, is superior to that of LDPC based timesharing codes while the best performance, when received transmissions are optimally decoded, is bounded by the timesharing limit.