Generalized LDPC codes with Reed-Solomon and BCH codes as component codes for binary channels

A generalized low-density parity check code (GLDPC) is a low-density parity check code in which the constraint nodes of the code graph are block codes, rather than single parity checks. In this paper, we study GLDPC codes which have BCH or Reed-Solomon codes as subcodes. The performance of the proposed scheme is investigated on a BEC and BSC for infinite and finite code lengths. The analysis shows that the performance of the scheme on a BEC is poor compared to that of LDPC codes. However, the performance on a BSC is competitive to that of LDPC codes. Furthermore, results of the finite length analysis on a BEC can be used under certain conditions as a tight lower bound on the performance of the scheme on a BSC.