Ensemble Weight Enumerators for Protograph-Based Generalized LDPC Codes

Abstract

Protograph-based LDPC codes have the advantages of a simple design (or search) procedure and highly structured encoders and decoders. These advantages have also been exploited in the design of protograph-based generalized LDPC (G-LDPC) codes. Recently, a technique for computing ensemble weight enumerators for protograph-based LDPC codes has been published. In the current paper, we extend those results to protograph-based G-LDPC codes. That is, we first derive ensemble weight enumerators for finite-length G-LDPC codes based on protographs, and then we consider the asymptotic case. The asymptotic results allow us to determine whether or not the typical minimum distance in the ensemble grows linearly with codeword length.