Capacity Optimality of AMP in Coded Systems

TL;DR

This paper proves that the AMP algorithm can achieve the capacity of large random matrix systems with arbitrary signals under certain conditions, supported by numerical results with LDPC codes and QPSK modulation.

Contribution

It establishes the capacity optimality of AMP in coded systems with arbitrary signal distributions, under a matching condition, extending previous results.

Findings

AMP achieves the constrained capacity when the matching condition is satisfied.

Optimized LDPC codes outperform un-matched codes under AMP.

QPSK modulation achieves BER within 1 dB of capacity limit.

Abstract

This paper studies a large random matrix system (LRMS) model involving an arbitrary signal distribution and forward error control (FEC) coding. We establish an area property based on the approximate message passing (AMP) algorithm. Under the assumption that the state evolution for AMP is correct for the coded system, the achievable rate of AMP is analyzed. We prove that AMP achieves the constrained capacity of the LRMS with an arbitrary signal distribution provided that a matching condition is satisfied. We provide related numerical results of binary signaling using irregular low-density parity-check (LDPC) codes. We show that the optimized codes demonstrate significantly better performance over un-matched ones under AMP. For quadrature phase shift keying (QPSK) modulation, bit error rate (BER) performance within 1 dB from the constrained capacity limit is observed.