On graphical representations of algebraic codes suitable for iterative decoding

In this paper, we describe two novel modifications of an algorithm for deriving sparse parity-check matrix representations of classical binary and non-binary algebraic codes. The proposed sparse representations are obtained by introducing a small number of auxiliary variables and check-equations that lead to Tanner graphs without four-cycles. When used with iterative decoding, the developed code representations show significant gain in performance when compared to other known description techniques.