Complexity-Optimized Irregular Decoders

Irregular decoding of low-density parity-check codes, i.e., using different algorithms in one iteration of the decoding of a single word, is studied. We formulate density evolution for irregular decoders. Using a one-dimensional representation of density evolution, we then jointly optimize irregular codes and irregular soft decoders for minimizing the decoding complexity. More specifically, for a given set of soft algorithms, a given channel, and a given code-rate, we find an irregular code-decoder pair which is capable of achieving a desired error performance with minimal decoding complexity. Robustness of irregular decoders when there exist channel estimation errors is also shown via an example