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AssigneeHuazhong University of Science and Technology
InventorsLi Peng, Si Jia Chen, Ying Long Shi, Ya Yu Gao, Bin Dai, Lin Zhang, Kun Liang, Bo Zhou
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The disclosure discloses an algebraic decoding method and a decoder for a (n, n(n−1), n−1) permutation group code in a communication modulation system. The basic principle of the decoding method is: assuming that two code elements p(r1)=s1 and p(r2)=s2 can be correctly detected in a received real vector with a length of n, including their element values s1, s2 and position indices r1, r2 in the vector, an intermediate parameter w is determined by solving an equation (r1−r2)w=(s1−s2)(mod n); and each code element is calculated by w according to p(i)=(s1+(n−r1+i)w)(mod n), i=1, 2, . . . , n. The decoder is mainly composed of multiple n-dimensional registers, a w calculator, n code element calculators, and a code element buffer. In the disclosure, in a case where a receiver only correctly detects two code elements in a transmitted codeword with a length of n, the codeword can be correctly decoded by using the received information of the two code elements.
An algebraic decoding method for a (n, n(n−1), n−1) permutation group code in a communication modulation system, wherein when n is a prime number, the (n, n(n−1), n−1) permutation group code contains n(n−1) permutation codewords, each of the permutation codewords contains n code elements, and a minimum Hamming distance between any two of the permutation codewords is n−1, comprising:
A decoder for a (n, n(n−1), n−1) permutation group code in a communication modulation system, comprising a plurality of independent n-dimensional registers, an intermediate parameter w calculator, n single-code-element calculators operating in parallel, and a n-dimensional buffer for n code elements,
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