Statistical physics of irregular low-density parity-check codes

Low-density parity-check codes with irregular constructions have recently b een shown to outperform the most advanced error-correcting codes to date. I n this paper we apply methods of statistical physics to study the typical p roperties of simple irregular codes. We use the replica method to find a ph ase transition which coincides with Shannon's coding bound when appropriate parameters are chosen. The decoding by belief propagation is also studied using statistical physics arguments; the theoretical solutions obtained are in good agreement with simulation results. We compare the performance of i rregular codes with that of regular codes and discuss the factors that cont ribute to the improvement in performance.