  In this paper, we present a belief propagation (BP) based algorithm for
decoding non-orthogonal space-time block codes (STBC) from cyclic division
algebras (CDA) having {\em large dimensions}. The proposed approach involves
message passing on Markov random field (MRF) representation of the STBC MIMO
system. Adoption of BP approach to decode non-orthogonal STBCs of large
dimensions has not been reported so far. Our simulation results show that the
proposed BP-based decoding achieves increasingly closer to SISO AWGN
performance for increased number of dimensions. In addition, it also achieves
near-capacity turbo coded BER performance; for e.g., with BP decoding of
$24\times 24$ STBC from CDA using BPSK (i.e., 576 real dimensions) and rate-1/2
turbo code (i.e., 12 bps/Hz spectral efficiency), coded BER performance close
to within just about 2.5 dB from the theoretical MIMO capacity is achieved.
