The Construction And Low-complexity Decoding Algorithms Of Low-density Parity-check Codes

Being a powerful class of error-correcting codes based on graphical models and iter-ative decoding algorithms, low-density parity-check(LDPC) codes have recently receivedmuch attention due to their capacity approaching performance and relatively low decodingcomplexity.This dissertation focus on the construction of quasi cyclic(QC) LDPC codes and thedeveloping of low-complexity decoding algorithms. Some main results are presented asfollows:(1) Two upper bounds on the minimum Hamming distance are derived for the nonbinaryQC LDPC codes whose parity-check matrices consist of weight-2columns. A specialbase matrix design allowing linear encoding in a parallel manner is also proposed.In addition, design principals are given, according to which parallel and efcientlyencodable codes with good Hamming distance distribution can be developed.(2) According to the minimum mean square error (MMSE) rule, the well-known Ja-cobian logarithm involved in LLR-SPA(log-likelihood ratio sum-product algorithm)can be approximated by choosing the proper frst-term Taylor’s series expansion,which can substantially reduced the decoding complexity. The simplifed algorithmhas better performance than that of both the normalized min-sum algorithm andthe ofset min-sum algorithm.(3) An efective message passing algorithm with linear computational complexity isproposed to count the number of the local shortest cycles in the parity check matricesof LDPC codes. During the procedure of constructing a QC LDPC code, each shiftvalue is assigned in an one-by-one fashion. By employing the algorithm, shift valueswhich maximize the average girth of variable nodes can be chosen efciently so thatthe performance of iterative decoding is improved.