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 polytope of the zeta function equals the fundamental cone of the code, which plays a crucial role in characterizing the performance of iterative decoding algorithms.