Low-Complexity Reliability-Based Iterative Decoding Algorithms For Binary LDPC Codes

LDPC (Low-density Parity-check Codes), discovered by Gallager in 1962, have been known as a class of Shannon limit approaching codes. This dissertation focuses on low-complexity reliability-based decoding algorithms for binary LDPC codes and their corresponding quantization methods. The main novelties and contributions of our work are summarized as follows.1. For the constructed Low-density Parity-check (LDPC) codes, an iterative decoding algorithm is presented which is designed based on syndrome messages. At check nodes, syndrome messages instead of extrinsic messages are calculated and passed back to variable nodes. This can save the computational complexities causing by the extrinsic messages computing. For doing so, it can reduce the memory load and facilitate hardware implementations.2. An iterative majority-logic decoding algorithm jointly using the column-weight ratio and the quantization parameters is presented, where the symdrome messages are still involved in check-node processing. Furthermore, we have designed the shifting direction and shifting step for the reliability measures. Simulation results show that, the presented algorithm can achieve good BER performance and fast decoding speed, even with small quantization levels (3-4 bits resolution).3. An iterative reliability-based majority-logic decoding algorithm is presented based on the configuration sets of processing variable nodes. The main computational loads of the presented algorithm include only binary logic and integer addition operations, resulting in low decoding complexity. Furthermore, by introducing the iterative set, a very small proportion (less than 6%) of variable nodes are involved in updating process, which can further reduce the computational complexity. Simulation results show that, the presented algorithm can achieve a good performance improvement, while it can significantly reduce the decoding complexity and memory load. Therefore, the presented algorithm can provide efficient trade-offs between performance and complexity.4. Uniform/non-uniform quantization methods are investigated and optimized. For the uniform quantization, we have presented a new design criterion to determine the quantization parameters and the quantizaion interval. Compared to the original parameters setting, the presented design criterion can achieve higher resolution and better quantizaion effect. For the non-uniform quantization, a new non-uniform quantization function is presented for received signals from different channel types, which can achive higer resolution for the signals falling around the decision threshold zero. Compared to the traditional quantization method, the new presented quantizaion scheme can work with smaller quantization level, while it can achieve better decoding performances.