Enhanced Iterative Decoding of Linear Block Codes

University Of Hawaii, Honolulu

Investigators

Abstract

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. The importance of these methods can be best realized by the fast integration of turbo codes in several standards and last year, an LDPC code was first selected in 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 related to the difficulty of evaluating the occurrence of an error floor, often too 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 also investigated. In addition, an iterative determination of the low weight profile of an LDPC code is proposed. Iterative decoding of codes rich of four-cycles in their graph representation has also been shown to perform well if a sufficiently redundant set of check 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 to cryptanalyse an iterative attack attack of the long standing McEliece public key cryptosystem.