Investigation of low-density parity-check codes and decoders

Abstract

Low-density parity-check (LDPC) codes have been proved to have theoretical limits approaching the channel capacity. Quasi-cyclic LDPC (QC-LDPC) codes are a particularly important class of LDPC codes. QC-LDPC codes have attracted much attention because of their special advantages, fexible design and ease of implementation. Recently, a novel type of QC-LDPC block codes called cyclically-coupled quasi-cyclic LDPC block codes (CC-QC-LDPC codes) have been proposed. CC-QC-LDPC code have been shown to achieve outstanding bit error performance with extremely low error floor. Our frst study is a novel construction method of CC-QC-LDPC codes which shortens the code length of CC-QC-LDPC codes and at the same time achieves a larger girth and a better error performance. We show that even with a shorter code length, the new CC-QC-LDPC codes can outperform the traditional CC-QC-LDPC ones. In our second study, we modify the CC-QC-LDPC code construction by using random permutation matrices instead of circulant permutation matrices, forming random-permutation-matrix-based CC-LDPC (RP-CC-LDPC) codes. Compared with CC-QC-LDPC codes, regular and irregular QC-LDPC codes, the BER performance of the RP-CC-LDPC code is comparable to and can possibly exceed that of other codes. However, decoder complexity and throughput are the major issues of the RP-CC-LDPC code. With an aim to solving the above problem, our third study proposes tree permutation matrices (TPM) and uses them to construct new types of LDPC codes. This kind of LDPC codes is named as tree-permutation-matrix LDPC (TPM-LDPC) codes. We also realize parallel decoding of TPM-LDPC codes using field-programmable gate-array (FPGA). Compared with random-permutation-matrix-based LDPC codes, the TPM-LDPC codes can achieve a higher throughput. Compared with QC-LDPC codes, the TPM-LDPC codes achieve a slightly better BER but requires a bit more resources in hardware implementation.