Concatenated permutation block codes for correcting single transposition errors

Permutation codes are advantageous due to their favourable symbol diversity properties and are applied in flash memories combined with rank modulation. Codebooks traditionally consist of permutations with specific distance properties. A class of permutation codes was presented where a codeword consists of a sequence or concatenation of permutations, rather than a single permutation. These codebooks were constructed to correct substitution or deletion errors. In this paper, permutations are concatenated to form codewords with the goal of detecting and correcting adjacent transposition errors. An outer code is used to detect erroneous permutations in the codeword, using additional parity permutations. The symbol diversity of permutation codes is preserved and codebooks with higher cardinalities are constructed which result in better code rates.