Improved Sum-Min Decoding for Irregular LDPC Codes

Abstract:
An analytical approach to determining the optimal post-processing function for the minimum operation in the Sum- Min algorithm, previously derived for regular Low-Density Parity-Check (LDPC) codes, is extended to irregular LDPC codes. The optimal post-processing expression for the irregular case varies from one check node to another as well as from one iteration to the next. For practical use, it is necessary to approximate this optimal function. Unlike for the regular case, where one could use a unique post-processing function throughout the decoding process without a loss of bit error performance, for irregular codes it is crucial to vary the post-processing from one iteration to the next in order to achieve good performance. Using this approach, a bit error performance of 0.15dB from the Sum-Product decoder was demonstrated, corresponding to a 1dB improvement compared to the Sum-Min algorithm without post-processing.