Statistical physics of regular low-density parity-check error-correcting codes

David Saad, Yoshiyuki Kabashima, Tatsuto Murayama +1 more

祥介 樺島, Yoshiyuki Kabashima

Renato Vicente, David Saad, Kabashima, Yoshiyuki

Low-density parity-check codes with irregular constructions have recently been shown to outperform the most advanced error-correcting codes to date. In this paper we apply methods of statistical physics to study the typical properties of simple irregular codes. We use the replica method to find a phase 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 irregular codes with that of regular codes and discuss the factors that contribute to the improvement in performance.

Renato Vicente, David Saad, Yoshyiuki Kabashima

Low-density parity-check codes with irregular constructions have recently been shown to outperform the most advanced error-correcting codes to date. In this paper we apply methods of statistical physics to study the typical properties of simple irregular codes. We use the replica method to find a phase 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 irregular codes with that of regular codes and discuss the factors that contribute to the improvement in performance.

祥介 樺島, Yoshiyuki Kabashima

Othman Omran Khalifa, Sheroz Khan, Mohamad Zaid +1 more

This paper mainly about the study on one of the widely used error correcting codes that is Low parity check Codes (LDPC). In this paper, the Regular LDPC code has been discussed The LDPC codes explained in this paper is about the Regular Binary LDPC codes or the Gallager.