Multiple access with distance preserving mappings for permutation codes

We present results for Distance Preserving Mappings (DPMs) for permutation codes that can be used for multiple access communication even under frequency jamming. We give examples of multiple codebooks that are DPMs such that each DPM can be assigned to a user for communication over a multiple access channel. We only consider one type of DPM called Distance Increasing Mappings (DIMs). The multiple access channel of interest is Time Division Multiple Access (TDMA). We show that it is possible to give a construction for DIMs that can be uniquely decoded even in the presence of frequency jamming. The DPMs are permutation codes found by mapping binary sequences to permutation sequences. The permutation codes have codewords of length M 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.