Enhanced Iterative Decoding of Linear Block Codes

在过去的十年中，迭代解码方法已经收到了很大的兴趣，由于惊人的错误性能，首先由Turbo码，最近由低密度奇偶校验（LDPC）码实现。这些方法的重要性可以通过Turbo码在几个标准中的快速集成来最好地实现，去年，LDPC码首次在标准会议上被选中。虽然最后的决定清楚地表明了成熟，但在LDPC码的实现中仍然存在一些问题，特别是对于许多通信系统中所需的中等长度。与LDPC码的实现相关的主要问题是难以评估错误平层的发生，通常太低而无法模拟。这项研究涉及的后处理技术，消除这些非MLD错误，一旦他们已经确定的发展，在这项研究中，新的解码方法，既减少了迭代次数，并改善目前的方法的错误性能也sofinvestigated。此外，还提出了一种迭代确定LDPC码的低重量轮廓的方法，如果使用足够冗余的校验和集，则对于图表示中富含四个循环的码的迭代解码也被证明是良好的。本研究发展一个模型，以评估在具有一定比例的四圈图上，迭代译码成功所需的冗余校验和的数目。本文的研究对于分析McEliece公钥密码体制的迭代攻击也是有用的。

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.