  We propose iterative detection and decoding (IDD) algorithms with Low-Density
Parity-Check (LDPC) codes for Multiple Input Multiple Output (MIMO) systems
operating in block-fading and fast Rayleigh fading channels. Soft-input
soft-output minimum mean-square error receivers with successive interference
cancellation are considered. In particular, we devise a novel strategy to
improve the bit error rate (BER) performance of IDD schemes, which takes into
account the soft \textit{a posteriori} output of the decoder in a block-fading
channel when Root-Check LDPC codes are used. A MIMO IDD receiver with soft
information processing that exploits the code structure and the behavior of the
log likelihood ratios is also developed. Moreover, we present a scheduling
algorithm for decoding LDPC codes in block-fading channels. Simulations show
that the proposed techniques result in significant gains in terms of BER for
both block-fading and fast-fading channels.
