A Generalization of Omura's Decoding Algorithm and a Proof of Convergence

An approximation of maximum-likelihood decoding over the binary symmetric channel was introduced by Omura in 1972. This decoder employs an iterative, randomized algorithm whose behavior closely mimics that of the simplex algorithm. In this paper, we generalize Omura's decoder to operate on an arbitrary binary-input memoryless channel. Further, we prove that the probability of the generalized Omura decoder (and hence Omura's original decoder) returning a maximum-likelihood codeword approaches 1 as the number of iterations goes to infinity, a result that has hereto remained unproven.