10-09-2020 дата публикации
Номер: US20200287774A1
The present disclosure provides an encoding method and an encoder for a (n, n(n−1), n−1) permutation group code in a communication modulation system, in which 2k-length binary information sequences are mapped to 2n-length permutation codeword signal points in a n-dimensional modulation constellation Γ. The constellation Γwith the coset characteristics is formed by selecting 2n-length permutation codewords from n(n−1) permutation codewords of a code set Pof the (n, n(n−1), n−1) permutation group code based on coset partition. The constellation Γis a coset code in which 2cosets are included and each coset includes 2permutation codewords, where k=k+k, and 2≤n(n−1). The present disclosure utilizes the coset characteristics to realize one-to-one correspondence mapping of the binary information sequence set to the permutation code constellation, so that the time complexity of executing the encoder is at most the linear complexity of the code length n. 1. An encoding method for a (n , n(n−1) , n−1) permutation group code in a communication modulation system , wherein the encoding method maps a k-length binary information sequence to a n-length permutation codeword in a signal constellation formed by the (n , n(n−1) , n−1) permutation group code based on coset partition , and comprises following steps of:{'sub': n,x', {'sub2': 'i'}], 'claim-text': [{'br': None, 'i': P', '=C', 'L', '={c', '∘l', '|c', '∈C', ',l', '∈L', ',i∈Z', ',j∈Z, 'sub': n,x', {'sub2': 'i'}, 'n', 'n,x', {'sub2': 'i'}, 'i', 'j', 'i', 'n', 'j', 'n,x', {'sub2': 'i'}, 'n', 'n−1, '}\u2003\u2003(1)'}, {'br': None, 'sub': rn', 'n,x', {'sub2': 'i'}, 'l1', 'n,x', {'sub2': 'i'}], 'sup': n−1', 'n−1, '={(t)L}={(t)L}\u2003\u2003(2)'}], '1) constructing the (n, n(n−1), n−1) permutation group code, 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 n(n−1) permutation codewords contains n code elements, a minimum Hamming distance between any two ...
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