  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.
