Memory AMP for Generalized MIMO: Coding Principle and Information-Theoretic Optimality

• Published in: IEEE transactions on wireless communications Vol. 23; no. 6; pp. 5769 - 5785
• Main Authors: Chen, Yufei, Liu, Lei, Chi, Yuhao, Li, Ying, Zhang, Zhaoyang
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.06.2024; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; capacity optimality; Codes; Coding; coding principle; Complexity; Complexity theory; Encoding; Error correcting codes; generalized MIMO (GMIMO); Information theory; low complexity; Matrices (mathematics); Memory approximate message passing (MAMP); Message passing; MIMO communication; Optimization; orthogonal/vector approximate message passing (OAMP/VAMP); Principles; Receivers; SISO (control systems); Wireless communication; Wireless communications
• ISSN: 1536-1276; 1558-2248
• DOI: 10.1109/TWC.2023.3328361

To support complex communication scenarios in next-generation wireless communications, this paper focuses on a generalized MIMO (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). The orthogonal/vector approximate message passing (OAMP/VAMP) receiver has been proved to be information-theoretically optimal in GMIMO, but it is limited to high-complexity linear minimum mean-square error (LMMSE). To solve this problem, a low-complexity memory approximate message passing (MAMP) receiver has recently been shown to be Bayes optimal but limited to uncoded systems. Therefore, how to design a low-complexity and information-theoretically optimal receiver for GMIMO is still an open issue. To address this issue, this paper proposes an information-theoretically optimal MAMP receiver and investigates its achievable rate analysis and optimal coding principle. Specifically, due to the long-memory linear detection, state evolution (SE) for MAMP is intricately multi-dimensional and cannot be used directly to analyze its achievable rate. To avoid this difficulty, a simplified single-input single-output (SISO) variational SE (VSE) for MAMP is developed by leveraging the SE fixed-point consistent property of MAMP and OAMP/VAMP. The achievable rate of MAMP is calculated using the VSE, and the optimal coding principle is established to maximize the achievable rate. On this basis, the information-theoretic optimality of MAMP is proved rigorously. Furthermore, the simplified SE analysis by fixed-point consistency is generalized to any two iterative detection algorithms with the identical SE fixed point. Numerical results show that the finite-length performances of MAMP with practical optimized low-density parity-check (LDPC) codes are <inline-formula> <tex-math notation="LaTeX">0.5 \sim 2.7 </tex-math></inline-formula> dB away from the associated constrained capacities. It is worth noting that MAMP can achieve the same performances as OAMP/VAMP with <inline-formula> <tex-math notation="LaTeX">4\% </tex-math></inline-formula> of the time consumption for large-scale systems.