Efficient Decoding Techniques for LDPC Codes

Efficient decoding techniques for LDPC codes are in demand, since these codes are included in many standards nowadays. Although the theoretical performance of LDPC codes is impressive, their practical implementation leads to problems like numerical inaccuracy, limited memory resources, etc. We investigate methods that are suited to reduce the decoding complexity while still keeping the loss in performance small. We aim to reduce the complexity using three approaches: simplification of the component decoders, restricting the message passing algorithm to binary variables and combining the LDPC decoder with other receiver tasks like demapping or multi-user detection. For the simplification of the component decoders, we analyze the min-sum algorithm and derive a theoretical framework which is used to explain previous heuristic approaches to improve the performance of this algorithm. Using this framework, we are able to modify the algorithm in order to achieve good performance for regular as well as irregular LDPC codes. Restricting all internal messages of an LDPC decoder to binary variables, leads to a significant reduction of memory requirements and allows the implementation of high-throughput decoders which are used for example in optical communication systems. We analyze binary message passing decoders using a general framework which is based on extrinsic information transfer charts. As special cases, we rederive Gallagers bit-flipping algorithm. Our derivation allows to generalize these algorithms for the case where soft-information from the channel is available, while still using binary variables for all internal messages. The analysis is used to derive bounds and to optimize LDPC codes for binary message passing decoders. Finally, we consider the optimization of an LDPC code where the decoder is not considered on its own, but in the context of a receiver structure which performs additional tasks like demapping or multi-user detection. We show how the code optimization can be performed efficiently by optimizing the degree distributions of variable and check nodes jointly. Our code optimization requires only knowledge of the extrinsic information transfer function of the receiver front-end, which can be obtained either analytically or via simulations. After a general derivation of the code optimization, we apply the optimization tools to iterative demapping and iterative multi-user detection.