Research On Construction And Decoding Performance Of Low-Density Parity-Check Codes

Low-density parity-check (LDPC) codes have been shown to form a class of Shannon limit approaching codes, and have become an attractive research area in the channel coding field recently. With the intensive research, LDPC codes have potential applications in the field such as wireless communication, ethernet, optical network and digital storage. In this dissertation, error floors of LDPC code and its iterative decoding algorithm are investigated. Some results are obtained and summarized as follow:1. The distribution of the number of short cycles in Tanner graphs of LDPC codes are investigated. An exact expression for the expected number of cycles in both regular and irregular LDPC code ensembles are derived. Asymptotically, we showed that the expected number of finite-length cycles is a constant and does not increase with block length.2. An algorithm for counting short cycles of Tanner graphs based on tree expanding is proposed. The proposed algorithm has the advantage of parallel implementation, and thus can count short cycles for relative long LDPC codes efficiently.3. Based on the investigation of the connectivity of Tanner graphs, an improved ACE algorithm based on EMD spectrum is proposed. The proposed algorithm can increase the stopping distance and minimum distance of the constructed codes, improve the error rate performance and reduce the error floor.4. According to the performance gap between the iterative decoding and maximum likelihood decoding algorithm, an improved iterative decoding algorithm is proposed. The proposed algorithm decreases the error rate performance considerably, whereas having almost the same complexity as the conventional iterative decoding algorithm.5. A novel method to eliminate small stopping sets in irregular LDPC codes is proposed. By adding several new check nodes and having their edges connected to small stopping sets in the original code, the improved code decreases the number of small stopping sets efficiently and reduces the error floors significantly.