Study On Non-binary LDPC Codes And Implementation Of The Codec

Low-density parity-check(LDPC) codes have been shown to have good error correcting performance that approaches the Shannon limit. Recently, LDPC codes have attracted considerable attention. Algorithms of encoding and decoding are proposed, some of which provide not only for theoretical research but also for hardware implementation. As a result, practical use of LDPC codes is of wide range, with their adoption as the first choice of channel coding scheme in various standards, DVB, WIMAX, etc. Extensive research shows that non-binary LDPC codes significantly exceed binary LDPC codes with short or moderate code-length or high order modulation. Consequently, this thesis investigates some key problems of non-binary LDPC codes.Non-binary QC-LDPC codes have some good characteristics such as simple encoding and low error rate, etc. In the thesis the methods of constructing and coding QC-LDPC codes are addressed in detail. Especially, two simplified constructions and their corrisponding encoding algorithms are given. Besides, the decoding algorithms such as the BP, FFT-BP, EMS, etc., are deeply studied. By theoretical analysis and simulation, we get some conclusions, that is, the FFT-BP version is simpler to implement than the original BP algorithm, with the same performance, while the EMS algorithm can greatly reduce the decoding complexity with a little performance loss.The FPGA implementation of non-binary LDPC codes is described in detail, combined with the “863” project,with an emphasis on the main techniques and modules involved in the design of the encoder and decoder. A particular encoding scheme with less memory resource and no pretreatment on parity-check matrix, completed through the parity-check matrix of the quasi-cyclic structure, is adopted. EMS algorithm is used in decoding scheme, which can greatly improve the speed of decoding.