Optimization With Exit Functions Of GLDPC-Staircase Codes For The BEC

In a previous work we introduced the Generalized LDPC-Staircase codes for the Binary Erasure Channel, based on LDPC-Staircase codes and Reed Solomon as component codes. In this paper we perform an asymptotic analysis, in terms of EXtrinsic Information Transfer functions and we de-rive an upper bound of the ML decoding threshold based on the area theorem. We use this analysis to study the impact of the internal LDPC-Staircase code rate on the performance, and show that the proposed Generalized LDPC-Staircase codes closely approach the channel capacity, with only a small number (E = 2, 3) of extra-repair symbols per check node. 1