Girth Detection Of Ldpc Codes And It's Application

Low-density parity-check (LDPC) codes have attracted much attention due to their Shannon-limit-approaching performance since rediscovered in 1996 and have become the hot-spot in channel coding field. LDPC codes have low error floor, simple decoder structures and fully parallel decoder implementation. The gap between the best designed LDPC code and the Shannon limit is only 0.0045dB. High encoding complexity of LDPC codes is getting reduced with further research and many low complexity encoding implementations come out and make practical use possible.The history of channel coding theory is first introduced in this thesis together with the main research aspects of LDPC codes. Based on the basic principles and concepts of LDPC codes, the constructions of parity-check matrixes and the encoding and decoding algorithms are detailed subsequently. A girth detection method of LDPC codes and its application are proposed and discussed in this thesis particularly.It's an important way to analyze the performance of LDPC codes with the parameters and feature of the parity-check matrixes. Factors related are the size of the parity-check matrixes, the row and column weight, girth and the number of short cycles in the matrixes. Girth is directly related to the minimum distance of the code and matrixes with higher girth will have better error-correcting ability. But it will be more difficult to construct parity-check matrixes when pursuing higher girth. Due to the short cycles in parity-check matrix, when decoded with iterative decoding method soft information comes out from a node will return back to itself after several iterations and so the performance is depressed.A girth detection method base on linked list is proposed in this thesis. A linked list is obtained by expanding the non-zero elements in parity-check matrixes into a layered structure. All the cycles can be detected by comparing nodes in different layers and the girth is the length of the shortest cycle. The exact number of different length of cycles is also given in the algorithm. Matrixes with different number of cycles are obtained using sub-block cyclic-shift factor replacing method and their performance is analyzed. Simulation results show that the number of cycle with special length affects the performance of the code only at a given signal-to-noise ratio (SNR). Matrixes with reduced number of the shortest length don't have performance improvement. Other parameters should be considered when analyzing and design the parity-check matrix such as minimum distance. Research focused on this issue isn't much at present and much more work can be done in the future.