Conditionally Cycle-Free Generalized Tanner Graphs: Theory and Application to High-Rate Serially Concatenated Codes
<|reference_start|>Conditionally Cycle-Free Generalized Tanner Graphs: Theory and Application to High-Rate Serially Concatenated Codes: 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.<|reference_end|>
@article{halford2006conditionally,
    title={Conditionally Cycle-Free Generalized Tanner Graphs: Theory and
  Application to High-Rate Serially Concatenated Codes},
    author={Thomas R. Halford and Keith M. Chugg},
    journal={arXiv preprint arXiv:cs/0611097},
    year={2006},
    archivePrefix={arXiv},
    eprint={cs/0611097},
    primaryClass={cs.IT math.IT}
}