This paper considers a generalized multiple-input multiple-output (GMIMO) with practical assumptions, such as massive antennas, practical channel coding, arbitrary input distributions, and general right-unitarily-invariant channel matrices (covering Rayleigh fading, certain ill-conditioned and correlated channel matrices). Orthogonal/vector approximate message passing (OAMP/VAMP) has been proved to be information-theoretically optimal in GMIMO, but it is limited to high complexity. Meanwhile, low-complexity memory approximate message passing (MAMP) was shown to be Bayes optimal in GMIMO, but channel coding was ignored. Therefore, how to design a low-complexity and information-theoretic optimal receiver for GMIMO is still an open issue. In this paper, we propose an information-theoretic optimal MAMP receiver for coded GMIMO, whose achievable rate analysis and optimal coding principle are provided to demonstrate its information-theoretic optimality. Specifically, state evolution (SE) for MAMP is intricately multi-dimensional because of the nature of local memory detection. To this end, a fixed-point consistency lemma is proposed to derive the simplified variational SE (VSE) for MAMP, based on which the achievable rate of MAMP is calculated, and the optimal coding principle is derived to maximize the achievable rate. Subsequently, we prove the information-theoretic optimality of MAMP. Numerical results show that the finite-length performances of MAMP with optimized LDPC codes are about 1.0 - 2.7 dB away from the associated constrained capacities. It is worth noting that MAMP can achieve the same performance as OAMP/VAMP with 0.4% of the time consumption for large-scale systems.

翻译：本文考虑具有实际假设的广义多输入多输出系统，例如大规模天线、实际信道编码、任意输入分布以及一般右酉不变信道矩阵（涵盖瑞利衰落、特定病态及相关信道矩阵）。正交/矢量近似消息传递（OAMP/VAMP）已被证明在广义MIMO中具有信息论最优性，但其复杂度较高。同时，低复杂度的记忆近似消息传递（MAMP）在广义MIMO中被证明是最优贝叶斯算法，但信道编码未被纳入考虑。因此，如何设计一个低复杂度且信息论最优的广义MIMO接收机仍是一个开放问题。本文提出了一种用于编码广义MIMO的信息论最优MAMP接收机，通过可达到速率分析与最优编码原理论证其信息论最优性。具体而言，由于局部记忆检测的特性，MAMP的状态演化（SE）呈现复杂的多维结构。为此，提出不动点一致性引理推导MAMP的简化变分SE（VSE），并基于此计算MAMP的可达速率，进而导出最大化可达速率的最优编码原理。随后，我们证明了MAMP的信息论最优性。数值结果表明，采用优化LDPC码的MAMP的有限长度性能与相应约束容量相差约1.0-2.7 dB。值得关注的是，在大规模系统中，MAMP仅需OAMP/VAMP的0.4%时间消耗即可实现相同性能。