Enhanced Iterative Decoding of Linear Block Codes

在过去的十年中，迭代译码方法由于首先由Turbo码和最近由低密度奇偶校验码(LDPC)获得的惊人的差错性能而受到极大的关注。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得到最好的体现，去年，在一次标准会议上首次选择了LDPC码。虽然最后这一决定明确表明已经成熟，但在LDPC码的实施中仍然存在一些问题，特别是对于许多通信系统所要求的中等长度的LDPC码。与LDPC码的实现相关的主要问题与评估差错平台的发生有关，该差错平台的出现通常太低，以至于难以模拟。这项研究涉及开发一种后处理技术，一旦识别出这些非MLD错误，就可以消除它们。在这项研究中，还研究了新的译码方法，既减少了迭代次数，又提高了现有方法的错误性能。此外，还提出了一种迭代确定LDPC码的低重量轮廓的方法，并证明了在充分冗余的校验和集合的情况下，迭代译码在图表示中具有丰富的四圈的情况下具有很好的性能。这项研究开发了一个模型来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。这一研究也有助于对长期存在的McEliess公钥密码体制的迭代攻击进行密码分析。

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.