Construction of Cyclic Codes Suitable for Iterative Decoding via Generating Idempotents

A parity check matrix for a binary linear code defines a bipartite graph (Tanner graph) which is isomorphic to a subgraph of a factor graph which explains a mechanism of the iterative decoding based on the sum-product algorithm. It is known that this decoding algorithm well approximates MAP decoding, but degradation of the approximation becomes serious when there exist cycles of short length, especially length 4, in Tanner graph. In this paper, based on the generating idempotents, we propose some methods to design parity check matrices for cyclic codes which define Tanner graphs with no cycles of length 4. We also show numerically error performance of cyclic codes by the iterative decoding implemented on factor graphs derived from the proposed parity check matrices. key words: Tanner graphs, cyclic codes, LDPC codes, sumproduct algorithm, iterative decoding

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