Analysis and Design of Moderate Length Regular LDPC Codes with Low Error Floors

The traditional method to estimate code performance in the higher SNR region is to use a sum of the contributions of the most dominant error events to the probability of error. If an ML decoder is used, these events will be minimum distance codewords; the traditional decoder used in LDPC codes, some variant of the message passing algorithm, will introduce non-codeword error events known as trapping sets. For long LDPC codes it is difficult to enumerate all of these dominant error events. A procedure to efficiently find dominant error events by using the regular low-density structure of an LDPC code is presented here. The search method can be adapted to work with LDPC codes of various regular and irregular degree distributions, but is especially suited to a very practical subset of LDPC known as regular {3, 6} codes of moderate block length. We also show how codes with very low error floors can be created by utilizing this search method.