LDPC code design for MMSE turbo equalization

The design of low density parity check (LDPC) codes with minimum mean squared error (MMSE) turbo equalization is considered. Techniques to compute the probability density function of the extrinsic information at the output of the equalizer and the decoder are discussed. Using these techniques, it is shown that thresholds can be computed for LDPC codes for intersymbol interference (ISI) channels and good LDPC code ensembles can be designed. The distinct features of this work include: (1) The input-output pdf of the equalizer is expressed in closed-form, and evaluated analytically - no simulation of the equalizer or the code is needed during the design process; (2) ISI channels with very long memory can be easily handled; (3) Codes for fading ISI channels can be designed without the need for extensive numerical computation.