Mathematics, Department of


Date of this Version



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.


Copyright 2004 IEEE. Used by permission.


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.

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