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. As a byproduct, we provide an alternative derivation for the constraint capacity of an LRMS using a proved property of AMP. We discuss realization techniques for the matching principle of binary signaling using irregular low-density parity-check (LDPC) codes and provide related numerical results. 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.

中文翻译：

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编码系统中 AMP 的容量优化


本文研究了涉及任意信号分布和前向错误控制（FEC）编码的大型随机矩阵系统（LRMS）模型。我们基于近似消息传递（AMP）算法建立区域属性。假设编码系统的 AMP 状态演化是正确的，分析了 AMP 的可实现速率。我们证明，只要满足匹配条件，AMP 就可以实现具有任意信号分布的 LRMS 的受限容量。作为副产品，我们使用 AMP 的已证明属性提供了 LRMS 约束容量的替代推导。我们讨论了使用不规则低密度奇偶校验（LDPC）码的二进制信令匹配原理的实现技术，并提供了相关的数值结果。我们表明，优化后的代码在 AMP 下表现出比不匹配的代码明显更好的性能。对于正交相移键控 (QPSK) 调制，观察到误码率 (BER) 性能与受限容量限制相差在 1 dB 以内。