We investigate the optimal Hamming distance that is achievable when mapping binary sequences to permutation sequences. This is used to determine how close to optimum some of the known mappings are. Furthermore, using simulation results we show that mappings found by exhaustive search using optimum distance as criterion perform better than previous known mappings

We introduce the new concept of permutation trellis codes and present a generalized construction procedure, applying our technique of distance-preserving mappings. Minimum-distance decoding follows naturally, using the Viterbi algorithm. We furthermore investigate the performance of these codes when combined with multitone frequency-shift keying modulation and noncoherent detection in a diversity scheme, to make transmissions robust against narrowband, broadband, and background noise disturbances, such as those encountered in power-line communications.