Good coupling between LDPC-staircase and Reed-Solomon for the design of GLDPC codes for the erasure channel

In this paper we analyze the design of Generalized LDPC-staircase (GLDPC-staircase) codes, where the base code is an LDPC-Staircase code and component codes are Reed-Solomon codes. More precisely we compare two schemes: scheme A has the property that on each check node of the base code the repair symbol generated by the LDPC code is also a Reed-Solomon repair symbol. On the opposite, with scheme B for each check node the repair symbols generated by the LDPC code are Reed-Solomon source symbols. In this work we perform a behavioral analysis of the two schemes in order to determine the best one for ITerative + Reed Solomon (IT+RS) and Maximum Likelihood (ML) decoding. To that purpose we use an asymptotic analysis using Density evolution (DE) and EXtrinsic Information Transfer techniques, as well as a finite length analysis. We show that scheme A is globally the best solution since it significantly performs better than scheme B with an (IT+RS) decoding and yields similar performance with ML decoding.