Pseudo-Codewords of Cycle Codes via Zeta Functions
<|reference_start|>Pseudo-Codewords of Cycle Codes via Zeta Functions: Cycle codes are a special case of low-density parity-check (LDPC) codes and as such can be decoded using an iterative message-passing decoding algorithm on the associated Tanner graph. The existence of pseudo-codewords is known to cause the decoding algorithm to fail in certain instances. In this paper, we draw a connection between pseudo-codewords of cycle codes and the so-called edge zeta function of the associated normal graph and show how the Newton polyhedron of the zeta function equals the fundamental cone of the code, which plays a crucial role in characterizing the performance of iterative decoding algorithms.<|reference_end|>
@article{koetter2005pseudo-codewords,
    title={Pseudo-Codewords of Cycle Codes via Zeta Functions},
    author={Ralf Koetter, Wen-Ching W. Li, Pascal O. Vontobel, Judy L. Walker},
    journal={arXiv preprint arXiv:cs/0502033},
    year={2005},
    archivePrefix={arXiv},
    eprint={cs/0502033},
    primaryClass={cs.IT math.IT}
}