  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 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
multidimensional and cannot be used directly to analyze its achievable rate. To
avoid this difficulty, a simplified single-input single-output 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. Numerical results show that the finite-length performances
of MAMP with practical optimized LDPC codes are 0.5-2.7 dB away from the
associated constrained capacities. It is worth noting that MAMP can achieve the
same performances as OAMP/VAMP with 0.4% of the time consumption for
large-scale systems.
