As compared to uncoded unitary space-time modulation (USTM), channel coded USTM has received increased attention for its large coding gain. However, low-density parity-check (LDPC) coded USTM has only received limited attention. This paper proposes a scheme of combining LDPC code with USTM for noncoherent MIMO communication system over Rayleigh flat fading and additive white Gaussian noise (AWGN) channel. At the receiver, considering the soft information required by the belief-propagation (BP) iterative decoder of the LDPC code, we deduce a low complexity maximum a posteriori probability (MAP) demodulating algorithm for a special USTM based on the sine-cosine function, SC-USTM for short. We combine the MAP with the maximum likelihood (ML) demodulating algorithm based on the SC-USTM in order to generate a novel dual-demodulator for further decreasing the computational complexity of the demodulating/decoding system. For improving the performance of the receiver, the iterative feedback scheme between the MAP demodulator and the BP decoder is designed. Comparing with the uncoded USTM, our LDPC-coded USTM can obtain about 15 - 17 dB coding gain at 10-5 BER.