  This paper investigates a large unitarily invariant system (LUIS) involving a
unitarily invariant sensing matrix, an arbitrary fixed signal distribution, and
forward error control (FEC) coding. Several area properties are established
based on the state evolution of orthogonal approximate message passing (OAMP)
in an un-coded LUIS. Under the assumptions that the state evolution for joint
OAMP and FEC decoding is correct and the replica method is reliable, we analyze
the achievable rate of OAMP. We prove that OAMP reaches the constrained
capacity predicted by the replica method of the LUIS with an arbitrary signal
distribution based on matched FEC coding. Meanwhile, we elaborate a constrained
capacity-achieving coding principle for LUIS, based on which irregular
low-density parity-check (LDPC) codes are optimized for binary signaling in the
simulation results. We show that OAMP with the optimized codes has significant
performance improvement over the un-optimized ones and the well-known Turbo
linear MMSE algorithm. For quadrature phase-shift keying (QPSK) modulation,
constrained capacity-approaching bit error rate (BER) performances are observed
under various channel conditions.
