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AssigneeHuazhong University of Science and Technology
InventorsLi PENG, Gaofeng LI, Jiaolong WEI, Kun LIANG, Bo ZHOU
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A construction method for a (n,n(n−1),n−1) permutation group code based on coset partition is provided. The presented (n,n(n−1),n−1) permutation group code has an error-correcting capability of d−1 and features a strong anti-interference capability for channel interferences comprising multi-frequency interferences and signal fading. As n is a prime, for a permutation code family with a minimum distance of n−1 and a code set size of n(n−1), the invention provides a method of calculating n−1 orbit leader permutation codewords by On={αo1}α=1n-1(mod n) and enumerating residual codewords of the code set by Pn=CnOn={(l1)n-1On}={(rn)n-1On}. Besides, a generator of the code set thereof is provided. The (n,n(n−1),n−1) permutation group code of the invention is an algebraic-structured code, n−1 codewords of the orbit leader array can be obtained simply by adder and (mod n) calculator rather than multiplication of positive integers. Composition operations of the cyclic subgroup Cn acting on all permutations oα of the orbit leader permutation array On are replaced by well-defined cyclic shift composite operation functions (l1)n-1 and (rn)n-1 so that the action of the cyclic group acting on permutations is realized by a group of cyclic shift registers.
A construction method of the (n,n(n−1),n−1) permutation group codes based on coset partition, wherein a construction of this permutation code with a code length of n, a minimum distance of n−1 and a code size of n(n−1) is expressed by Pn={{pβ60}β=1n}α=1n-1=CnOn={{Cno1}, {Cno2}, . . . , {Cnon-1}}={{cβ∘oα}β=1n}α=1n-1, Pn=CnOn represents that Cn is a coset of the subgroup On and On is also a coset of the subgroup Cn, Pn={{Cno1}, {Cno2}, . . . , {Cnon-1}} represents dividing Pn into n−1 cosets by the subgroup Cn, each coset {Cnoα} forms an orbit or an cyclic Latin square (C-LS) of a permutation oα, Pn={{pβα}β=1n}α=1n-1={{cβ∘oα}β=1n}α=1n-1 represents a permutation code and each codeword pβα is generated by composition operation of a permutation cβ of the subgroup Cn and a permutation oα of the subgroup On, α=1, 2, . . . n−1, and β=1, 2, . . . n.
A generator of the (n,n(n−1),n−1) permutation group code based on coset partition, comprising an orbit leader array generator, a flash memory and a cyclic-bidirectional-shift register group, wherein
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