Le décodage pondere en tant que procédé de réévaluation d’une distribution de probabilité

We propose to redefine weighted decoding of a redundant code as consisting of reestimating a given prior probability distribution in order to take into account the code constraints. The optimum solution of this problem results from using the « minimum cross-entropy » principle and is shown to coincide with the computation of the probabilities to be compared in order to perform maximum likelihood decoding when the prior distribution is exactly known. The principle however also holds when the prior distribution is approximate or biased, which explains the robustness of decoding with respect to weighting information. Such a redefinition also enables using the intermediate steps of decoding, in the case of codes associated by concatenation or product, as a source of weighting information for the subsequent steps. One is led for simplicity’s sake to an estimate of the posterior probability in separable form with respect to the information symbols ; its definition is given and certain of its applications are discussed.