The Study Of The Algebraic Structure Design Method Of Permutation Codes

Permutation codes are a class of multi-band error correcting codes. They are not conventional multi-band linear codes, with each code symbol appears just once. Compared with the traditional binary codes, the permutation codes enjoys higher error correcting performance under the circumstance that the permutation code has the same least Hamming distance as the traditional binary codes. For convenience of implementing the construction of permutation codes with larger least Hamming distance using software as well as hardware, I will try to construct them in algebraic method.This paper makes a deep study of the structures of the permutation codes on the basis of the theoretical research results of the boundary of the permutation codes. According to the search scheme of the complete permutation arrays based on the existing shift operation function, in the cyclic Latin, I have found the structure features of the permutation codes whose codes length is n and its least Hamming distance is n-1 and the cardinality is n(n-1) when n is a primer.This paper presents a scheme, in which the algebraic construction of the permutation codes whose length is n and its least Hamming distance is n-1, and the cardinality is n(n-1) when n is a primer is presented. After the construction, in this paper, the scheme is combined with the M-FSK modulation technique, constructing Time-Frequency Shift Keying(TFSK) transceiver. This program introduces time diversity as well as frequency diversity simultaneously, making it enjoy fairly strong robustness against multi-frequency noise, colored background noise and impulse noise.Finally, the simulation analysis of the performance of its anti-jamming against these kinds of jamming is presented.This paper introduces the concepts of the linear constrained permutation codes.By adding constraints, we can narrow the scope of the permutation codewords satisfying the constraints, so as to reduce the time complexity of finding the optimal permutation code.Then the constrainted permutation codes are extended to multipermutation codes and multipermutation arrays.On the basis,I will apply the permutation codes I construct with algebraic scheme to the AWGN channel to make simulation, in order to validate the performance of it on AWGN channel.Due to the fact that the permutation code we construct with algebraic method possesses good algebraic properties, each code word can be obtained by the row index and the column index as well as the cyclic shift of the permutation code, so this kind of permutation code could be easily implemented using hardware. Because of the good distance properties of this class of permutation codes, it is easy for us to design the encoder from binary codes to permutation codes.