Constructing LDPC Codes by 2-Lifts

With the motivation of constructing Low-Density Parity-Check (LDPC) codes with low error floors, we propose a new code construction scheme based on random 2-lifts. An analysis on stopping set distributions of the proposed code ensembles is presented. The analysis shows that low-weight stopping sets in the resulting codes are typically the results of stopping sets with weak graph expansion properties in the base graphs. Based on this analysis, we propose a set of design criteria for constructing codes with low error floors. According to the design criteria, stopping sets with weak graph expansion properties should be avoided in the base graphs. We present numerical results on constructing capacity-approaching codes over Binary Erasure Channels (BEC). The numerical results show that the codes by the proposed scheme have significantly lower error floors compared with the codes by the standard construction.