Abstract by Spencer Giddens
Optimization of LDPC Codes of Small Block Length
Current methods for optimization of low-density parity-check (LDPC) codes optimize the degree distribution pairs asymptotically as block length approaches infinity. This effectively ignores the discrete nature of the space of valid degree distribution pairs for LDPC codes of finite block length. Since only finite block lengths are attainable in practice, the results of these methods can only be used approximately in any real code. For large block lengths, the difference between the optimal pair generated theoretically and the approximate pair used in practice is negligible. As the block length decreases, however, this difference becomes more pronounced, making noticeably suboptimal performance more likely for small to medium block lengths. We present and analyze an algorithm for completely enumerating the space of all valid degree distribution pairs for a given fixed block length and coding rate. We then demonstrate this algorithm on an example LDPC code of finite block length. Finally, we discuss how the result of this algorithm can be utilized by discrete optimization routines to form a new method for optimization of finite block length LDPC codes.