Pseudo-Codewords of Cycle Codes via Zeta Functions
Information Theory
2007-07-16 v1 math.IT
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.
Keywords
Cite
@article{arxiv.cs/0502033,
title = {Pseudo-Codewords of Cycle Codes via Zeta Functions},
author = {Ralf Koetter and Wen-Ching W. Li and Pascal O. Vontobel and Judy L. Walker},
journal= {arXiv preprint arXiv:cs/0502033},
year = {2007}
}
Comments
Presented at Information Theory Workshop (ITW), San Antonio, TX, 2004