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Pseudo-Codewords of Cycle Codes via Zeta Functions

Ralf Koetter·Wen-Ching W. Li·Pascal O. Vontobel·Judy L. Walker
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Abstract

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.

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Ralf Koetter, Wen-Ching W. Li, Pascal O. Vontobel, Judy L. Walker. 2005-02-06. Pseudo-Codewords of Cycle Codes via Zeta Functions. https://arxiv.org/abs/cs/0502033

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