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Conditionally Cycle-Free Generalized Tanner Graphs: Theory and Application to High-Rate Serially Concatenated Codes

Thomas R. Halford·Keith M. Chugg
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Abstract

Generalized Tanner graphs have been implicitly studied by a number of authors under the rubric of generalized parity-check matrices. This work considers the conditioning of binary hidden variables in such models in order to break all cycles and thus derive optimal soft-in soft-out (SISO) decoding algorithms. Conditionally cycle-free generalized Tanner graphs are shown to imply optimal SISO decoding algorithms for the first order Reed-Muller codes and their duals - the extended Hamming codes - which are substantially less complex than conventional bit-level trellis decoding. The study of low-complexity optimal SISO decoding algorithms for the family of extended Hamming codes is practically motivated. Specifically, it is shown that exended Hamming codes offer an attractive alternative to high-rate convolutional codes in terms of both performance and complexity for use in very high-rate, very low-floor, serially concatenated coding schemes.

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Thomas R. Halford, Keith M. Chugg. 2007-03-26. Conditionally Cycle-Free Generalized Tanner Graphs: Theory and Application to High-Rate Serially Concatenated Codes. https://arxiv.org/abs/cs/0611097

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