  We propose an Iterative Detection and Decoding (IDD) scheme with Low Density
Parity Check (LDPC) codes for Multiple Input Multiple Output (MIMO) systems for
block-fading $F = 2$ and fast fading Rayleigh channels. An IDD receiver with
soft information processing that exploits the code structure and the behaviour
of the log likelihood ratios (LLR)'s is developed. Minimum Mean Square Error
(MMSE) with Successive Interference Cancellation (SIC) and with Parallel
Interference Cancellation (PIC) schemes are considered. The soft \textit{a
posteriori} output of the decoder in a block-fading channel with Root-Check
LDPC codes has allowed us to create a new strategy to improve the Bit Error
Rate (BER) of a MIMO IDD scheme. Our proposed strategy in some scenarios has
resulted in up to 3dB of gain in terms of BER for block-fading channels and up
to 1dB in fast fading channels.
