Décodage par répliques

The very redundancy of a message enables to recover each symbol in terms of several partial contexts; in other words, it is possible to compute several replicas of each symbol in terms of other ones. Decoding of redundant codes is interpreted according to this viewpoint. A convenient formalism results in the statement of the maximum-likelihood decision rule on a symbol, given a set of its replicas, in the binary case. It is first applied to linear block codes. The decision rule which takes into account all possible replicas is expressed in terms of an exhaustive set of replicas, derived from the parity check matrix of the code. A modification of the decision rule, which saves its general shape, makes its result coincide with that of word-by-word maximum-likelihood decoding; besides, it simplifies this decision rule. Restricting the set of replicas taken into account also affords simplification of decoding, at the expense of optimality. It results in threshold decoding for orthogonalisable codes. The case of convolutional codes is more briefly discussed. The main specific problems are then the restriction to a finite context and the extension of the decision rule to non-systematic codes.