Concatenated permutation block codes based on set partitioning for substitution and deletion error-control

A new class of permutation codes is presented where, instead of considering one permutation as a codeword, codewords consist of a sequence of permutations. The advantage of using permutations, i.e. their favourable symbol diversity properties, is preserved. Additionally, using sequences of permutations as codewords, code rates close to the optimum rate can be achieved. Firstly, the complete set of permutations is divided into subsets by using set partitioning. Binary data is then mapped to permutations from these subsets. These permutations, together with a parity permutation, will form the codeword. Two constructions will be presented: one capable of detecting and correcting substitution errors and the other capable of detecting and correcting either substitution or deletion errors.