| In 1962, Gallager invented an error correcting code, Low Density Parity Check Code. This kind of code decodes effectively and maintains a linear relationship between decode complexity and code length when code length is long, because of sparseness of the check-up matrix. LDPC codes performance close to Shannon limit, so it becomes hot spot in channel coding field. Researchers proposed various methods to reduce high encoding complexity of LDPC codes, which makes LDPC code practical use possible. In this thesis firstly introduce the development history of channel encoding, then introduce the principles of LDPC code, including the structure of check-up matrix, coding algorithm and decoding algorithm, at last research the LDPC codes of IEEE802.16e.In this thesis, LDPC decoding algorithms are researched. On BP algorithms, BP, LLR BP, UMP BP-Based, Normalized BP and Offset BP algorithm are studied and simulated. An improved BP algorithm was proposed, using multiplicative factor to compensate the correlation between message nodes, which compensates the shortcomings of LDPC codes with short cycles. On bit-flipping algorithm, the criteria for bit flipping in IMWBF algorithm and RRWBF algorithm are summarized, and a multi-bit flipping algorithm is proposed on considering the reliability ratio and absolute value of symbol. In this algorithm, multi-bit are flipping per iteration, making decoding faster, gaining lower BER with the same iterations. LDPC codes of IEEE802.16e are also researched in this thesis. The check matrix of LDPC codes have quasi-cyclic structure, and use the quasi-diagonal sub-matrix to iterative encoding. LDPC code with 1/2 code rate is simulated using the improved BP and BF decoding algorithm. The result shows that improved BP algorithm is better than LLR BP algorithm and the BF algorithm. On the same code rate condition, the code with longer length has better performance, and on the same code length condition, the code with bigger code rate has better performance. |
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