Pseudo-Codewords of Cycle Codes via Zeta Functions

Authors

Ralf Koetter, University of Illinois at Urbana-ChampaignFollow
Wen-Cheng W. Li, Pennsylvania State University - Main CampusFollow
Pascal O. Vontobel, University of Wisconsin-MadisonFollow
Judy L. Walker, University of Nebraska - LincolnFollow

Document Type

Article

Date of this Version

2005

Citation

http://arxiv.org/abs/cs/0502033v1

Presented at Information Theory Workshop (ITW), San Antonio, TX, 2004.

Published in Proceedings of the IEEE Information Theory Workshop, San Antonio, TX, Oct. 24-29, 2004.

Comments

Copyright 2004 IEEE. Used by permission.

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 decod- ing 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 de- coding algorithms.