Iterative min-sum decoding of tail-biting codes

By invoking a form of the Perron-Frobenius theorem for the "min-sum" semi-ring, we obtain a union bound on the performance of iterative decoding of tail-biting codes. This bound shows that for the Gaussian channel, iterative decoding will be optimum, at least for high SNRs, if and only if the minimum "pseudo-distance" of the code is larger than the ordinary minimum distance.