Analysis of Generalized LDPC Codes with Random Component Codes for the Binary Erasure Channel

In this paper, a method for the asymptotic analysis of generalized low-density parity-check (GLDPC) codes on the binary erasure channel (BEC) is proposed. The considered GLDPC codes have block linear codes as check nodes. Instead of considering specific check component codes, like Hamming or BCH codes, random codes are considered, and a technique is developed for obtaining the expected check EXIT function for the overall GLDPC code. Each check component code is supposed to belong to an expurgated ensemble. Some GLDPC thresholds obtained by this technique are compared with those of GLDPC codes, with the same distribution and component codes lengths, using specific codes. Results obtained by combining our analysis with differential evolution tool are also presented.