Improved low-density parity-check codes using irregular graphs and belief propagation

We construct new families of 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 codes. Our improved performance comes from using codes based on irregular random bipartite graphs, based on the work of Luby et al. (1997). Previously studied low-density codes have been derived from regular bipartite graphs. Initial experimental results for our irregular codes suggest that, with improvements, irregular codes may be able to match turbo code performance.