The effect of Hamming distances on permutation codes for multiuser communication in the power line communications channel

We partition permutation sequences into groups to form permutation codes for multiuser communication. Each group becomes a codebook for each user in a multiuser communication system. We present simulation results for the performance of different partitions of permutation codes for multiuser communication, where the codes are to be used in channels with background noise and jamming, such as the Power Line Communications (PLC) channel. With the help of the simulation results, we show that by partitioning codebooks according to distance properties we can affect the performance of the codes. The permutation codes have codewords of lengthM with symbols taken from an alphabet whose cardinality is M, where M is any integer. Each symbol may be seen as representing one out of the M frequencies in an M-ary Frequency Shift keying modulation scheme, for example. Each user has a codebook of cardinality greater or equal to M and there can be a maximum of M - 1 users communicating at the same time through a multiple access OR channel.