| Iterative decoding techniques have been receiving more and more attentions with the invention of turbo codes and the rediscovery of low-density parity-check (LDPC) codes. An important aspect in the study of iterative decoding is the tradeoff between decoding performance and complexities. For both LDPC codes and turbo codes, optimum decoding algorithms can provide very good performance. However, complicated operations are involved in the optimum decoding, and prohibit the wide applications of LDPC codes and turbo codes in the next generation digital communication and storage systems.; This research investigates the reduced complexity decoding algorithms of LDPC codes and turbo codes. For decoding LDPC codes, new algorithms, namely the normalized BP-based algorithm and the offset BP-based algorithm, are proposed. Density evolution algorithms are derived and are used to determine the best decoder parameters associated with each of the algorithms. Both numerical results and simulations show that the new algorithms can achieve near optimum decoding performances. In addition to the advantage of low computational complexities, the two new algorithms are less subject to quantization errors and correlation effects than the optimum BP algorithm, and are more suitable for hardware implementation. For a special kind of LDPC codes—the geometric LDPC codes, we propose the normalized APP-based algorithm, which is even more simplified yet still can achieve the near optimum performance. For decoding turbo codes, two new sub-optimum decoding algorithms are proposed. The first is the bi-directional soft-output Viterbi algorithm (bi-SOVA), which is based on utilizing a backward SOVA decoding in addition to the conventional forward one. The second is the normalized Max-Log-MAP algorithm, which improves the performance of the Max-Log-MAP decoding by scaling the soft outputs with some predetermined factors. |
