  With the complication of future communication scenarios, most conventional
signal processing technologies of multi-user multiple-input multiple-output
(MU-MIMO) become unreliable, which are designed based on ideal assumptions,
such as Gaussian signaling and independent identically distributed (IID)
channel matrices. As a result, this paper considers a generalized MU-MIMO
(GMU-MIMO) system with more general assumptions, i.e., arbitrarily fixed input
distributions, and general unitarily-invariant channel matrices. However, there
is still no accurate capacity analysis and capacity optimal transceiver with
practical complexity for GMU-MIMO under the constraint of coding. To address
these issues, inspired by the replica method, the constrained sum capacity of
coded GMU-MIMO with fixed input distribution is calculated by using the
celebrated mutual information and minimum mean-square error (MMSE) lemma and
the MMSE optimality of orthogonal/vector approximate message passing
(OAMP/VAMP). Then, a capacity optimal multiuser OAMP/VAMP receiver is proposed,
whose achievable rate is proved to be equal to the constrained sum capacity.
Moreover, a design principle of multi-user codes is presented for the multiuser
OAMP/VAMP, based on which a kind of practical multi-user low-density
parity-check (MU-LDPC) code is designed. Numerical results show that
finite-length performances of the proposed MU-LDPC codes with multi-user
OAMP/VAMP are about 2 dB away from the constrained sum capacity and outperform
those of the existing state-of-art methods.
