Enhanced Iterative Decoding of Linear Block Codes

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Over the past decade, iterative decoding methods have received a great deal of interest due to the astonishing error performances achieved first by turbo codes, and more recently by low-density parity check (LDPC) codes. Theimportance of these methods can be best realized by the fast integration ofturbo codes in several standards and last year, an LDPC code was first selectedin a standard meeting. Although this last decision clearly indicates maturity, several issues remain problematic in the implementation of LDPC codes, especially for moderate lengths, which are required in many communications systems. The main problem associated with the implementation of LDPC codes is relatedto the difficulty of evaluating the occurrence of an error floor, oftentoo low to be simulated. This research involves the development of a postprocessing technique which eliminates these non MLD errors once they have been identified.In this research, new decoding methods which both reduce the number of iterations and improve the error performance of current approaches are alsoinvestigated. In addition, an iterative determination of the low weight profileof an LDPC code is proposed.Iterative decoding of codes rich of four-cycles in their graph representationhas also been shown to perform well if a sufficiently redundant set ofcheck sums is used. This research develops a model to evaluate the number of redundant check sums needed for iterative decoding to succeed on a graph with a certain proportion of four-cycles. This study is also useful tocryptanalyse an iterative attack attack of the long standing McEliece public key cryptosystem.