This paper studies a large random matrix system (LRMS) model involving an arbitrary signal distribution and forward error control (FEC) coding. The authors 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. They prove that AMP achieves the constrained capacity of the LRMS with an arbitrary signal distribution provided that a matching condition is satisfied. As a byproduct, the authors provide an alternative derivation for the constraint capacity of an LRMS using a proved property of AMP. They discuss realization techniques for the matching principle of binary signaling using irregular low-density parity-check (LDPC) codes and provide related numerical results. They 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. 

　　Publication: 

　　-    IEEE Transactions on Information Theory, 67, 7, 4429-4445 (2021). 

　　Authors: 

　　-    Lei Liu (Japan Institute of Science and Technology) 

　　-    Chulong Liang (ZTE Corporation) 

　　-    Junjie Ma (Institute of Computational Mathematics and Scientific/Engineering Computing, AMSS, Chinese Academy of Sciences) 

　　-    Li Ping (City University of Hong Kong)