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

A method for the asymptotic analysis of doublygeneralized low-density parity-check (D-GLDPC) codes on the binary erasure channel (BEC) is described. The proposed method is based on extrinsic information transfer (EXIT) charts. It permits to overcome the impossibility to evaluate the EXIT function for the check or variable component codes, in situations where the information functions or split information functions for the component code are unknown. According to the proposed method, D-GLDPC codes where the check and variable component codes are random codes from an expurgated ensemble, are considered. A technique is then developed which permits to obtain the EXIT chart for the overall D-GLDPC code, by evaluating the expected EXIT function for each check and variable component code. This technique is then combined with differential evolution (DE) algorithm in order to generate some optimal D-GLDPC degree distributions. Numerical results on long, random codes, are presented which reveal how DGLDPC codes can outperform standard LDPC codes in terms of both waterfall performance and error floor.