Short-length LDPC Codes with Power-law Distributed Variable-node Degrees

In the design of low-density-parity-check (LDPC) codes, it has been proven that codes with variablenode and check-node degree distributions optimized by the “Density Evolution” (DE) algorithm can accomplish theoretical error performance very close to the Shannon limit. But the use of the DE algorithm requires two basic assumptions — infinite code length and infinite number of iterations performed by the decoder. Unfortunately, neither requirement can be fulfilled in practice. When the LDPC code has a finite length, say a few thousand symbols, the “DE-optimized” degree distributions may not be the best solutions. In this paper, we propose constructing shortlength LDPC codes with variable-node degrees following power-law distributions. We show that the proposed scalefree LDPC (SF-LDPC) codes, when compared with codes constructed with “DE-optimized” degree distributions, can achieve lower complexity (in terms of average number of node degrees), faster convergence time (in terms of number of iterations executed at the decoder) and similar/lower error rates.