The implementable decoders and large collection of data transmission and storage channels can be admitted at the same time using low density parity check (LDPC) group of Linear block codes. We will review some of the LDPC construction techniques and encoding problem for LDPC codes. Also certain special classes of LDPC codes which will resolve encoding problems will be introduced. Performance analysis and design optimization of LDPC coded multiple input multiple output(MIMO) orthogonal frequency division multiplexing(OFDM) has been considered. The tools of density evolution with mixture Gaussian approximations are used to optimize LDPC codes which are not regular and to compute minimum operational signal-to-noise ratios (SNRs) for ergodic MIMO-OFDM channels. In particular, the optimization is done for various MIMO-OFDM system configurations, which include a different channel models and different demodulation schemes; the performance which is optimized is checked with the corresponding channel capacity. The iterative message passing decoding algorithm which gives optimal performance will be presented. The performance of turbo-iterative receiver that consists of a soft maximum a posteriori (MAP) demodulator will be presented. From the LDPC profiles that already are optimized for ergodic channels, we construct small block-size irregular codes for outage MIMO-OFDM channels. © 2016 IEEE.