Principles Of LDPC Code And Study Of Multi-rate Coding

Since Turbo codes show excellent performance in the field of channel coding, Low-densityparity-check (LDPC) codes are nowadays at the center of attention of the coding researchcommunity after have been forgotten for nearly30years. LDPC codes is a class of good codewhich performance is close to the Shannon limit, As the codes get longer the performance becomebetter. Compare with Turbo codes, LDPC codes have several distinct advantages:1)(BeliefPropagation, BP) decoding for LDPC codes is fully parallelizable and can potentially beaccomplished at significantly greater speeds;2) LDPC decoding is verifiable in the sense thatdecoding to a correct codeword is a detectable event;3) low complexity decoder;4) good blockerror ratio(BLER) performance;5) the lower “error-floor” region.Currently there are two methods to construct LDPC codes: randomly constructed LDPC andstructured construct LDPC.protograph LDPC codes is a structured structure, It is a kind ofquasi-cyclic LDPC codes which has a character of low coding complexity. In addition, there areshort cycles in the Tanner graph of LDPC codes which will have a bad effect on decoding, So weshould study on the short cycles.Aiming at reducing coding complexity and improving the girth impact on the LDPC codedecoding, the main research paper have done is as follows:1、Firstly, make a brief review on the background of research of LDPC codes, Systematicallyexplan the definition of LDPC codes, Summarizes the common method of construction LDPCcodes, make a detailed description of the (Belief Propagation, BP) decoding algorithm principle,Introduce the evolutionary theory which can be used to find the the outstanding densitydistribution.2、Firstly study the presence of short cycles in LDPC code and how they affect the performanceof LDPC codes decoding, and then introduced the principle of protograph LDPC codes, Finally,based on these studies, proposes a low-complexity design method for cancelling length4cycles inthe factor graph of LDPC codes. The method is based on protograph, by a simple“copy-and-permute”algorithm, it can be applied to constructing different code rate LDPC codes.The simulation results in AWGN channels show that the performance of the proposed multi-rateLDPC codes have a certain improvement than that of random generated LDPC codes, and has anadvantage over PEG designed LDPC codes in some certain SNR range.3、Firstly introduce the PEG algorithm in detail which can increase the girth of the constructedcodes, and then a method for constructing parity-check matrices of LDPC codes with large girth by progressively establishing non-zero entry in an entry-by-entry manner,which is based onoptimizing the number distribution of cycles of each non-zero entry.The simulation show that afteroptimization, length8cycles decreased and length10cycles increased which means the averagegirth is promoted, BER simulation shows the optimized LDPC codes has an advantage over PEGdesigned LDPC codes in some certain SNR range.