In this letter, a new reliability-based iterative majority-logic decoding (RBI-MLGD) algorithm that computes the extrinsic information of previous iterations of the variable node is proposed. This decoding algorithm is called historicalextrinsic reliability-based iterative decoder (HE-RBID) and improves the bit-error-rate performance of the previous RBI-MLGD. HE-RBID is particularly interesting for codes with a low degree of variable node, where traditional RBI-MLGD algorithms do not provide a good behavior. HE-RBID ensures a good performance without searching for the minimum at the check node and only by exchanging 1-bit messages between variable and check nodes.

This work was supported by the Spanish Ministerio de Ciencia e Innovacion under Grant TEC2011-27916. The work of J. M. Catala-Perez was supported by an FPI grant under Grant BES-2012-052130. The work of F. Garcia-Herrero was supported by an FPU grant sponsored by the Spanish Ministerio de Educacion under Grant AP2010-5178. The associate editor coordinating the review of this paper and approving it for publication was H. Saeedi.