Low-Complexity and Information-Theoretic Optimal Memory AMP for Coded Generalized MIMO

Abstract: 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.