Progressive Matrix Growth Algorithm for Constructing Rate-Compatible Length-Scalable Raptor-Like Quasi-Cyclic LDPC Codes

Abstract

With the worldwide deployment and rapid development of digital television terrestrial broadcasting (DTTB) systems, the demands of diversified multimedia services from the fixed/mobile receptions increase significantly. To satisfy the various requirements of quality of service, the forward error correction codes with multiple code rates and lengths become a trend for DTTB standards. In this paper, rate-compatible length-scalable raptor-like quasi-cyclic low density parity check (RL-QC-LDPC) codes are proposed for future DTTB systems, where a wide range of code rates and information/parity block lengths can be obtained with low implementation complexity. A low-complexity construction method, called progressive matrix growth (PMG), is also proposed for such kind of RL-QC-LDPC codes. Unlike conventional construction methods, PMG performs 2-D progressive extension of both information variable nodes and check nodes with limited computational complexity and memory resources. Based on the performance prediction provided by the tool of multi-edge type density evolution, several code families are constructed with PMG as examples, and careful discussions on design parameters are given. The numerical results show that the average gaps of SNR threshold to Shannon limit of binary-input additive white Gaussian noise channel are only 0.41~0.44 dB for the code families with information-bit puncturing.