Improved Low-Density Parity-Check Codes Using Irregular Graphs and Belief Propagation

We construct new families of error-correcting codes based on Gallager’s low-density parity-check codes, which we call irregular codes. When decoded using belief propagation, our codes can correct more errors than previously known low-density parity-check codes. For example, for rate 1/4 codes on 16,000 bits over a binary symmetric channel, previous low-density parity-check codes can correct up to approximately 16% errors, while our codes can correct over 17%. Our improved performance comes from using codes based on irregular random bipartite graphs, based on the work of [7]. Previously studied low-density parity-check codes have been derived from regular bipartite graphs. We report experimental results for our irregular codes on both binary symmetric channels and Gaussian channels. In some cases our results come very close to reported results for turbo codes, suggesting that, with improvements, irregular codes may be able to match turbo code performance.