Abstract: 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.

Abstract: 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 k-length binary information sequences are mapped to 2k n-length permutation codeword signal points in a n-dimensional modulation constellation ?n. The constellation ?n with the coset characteristics is formed by selecting 2k n-length permutation codewords from n(n?1) permutation codewords of a code set Pn,xi of the (n, n(n?1), n?1) permutation group code based on coset partition. The constellation ?n is a coset code in which 2k1 cosets are included and each coset includes 2k2 permutation codewords, where k=k1+k2, and 2k?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.

Abstract: 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.

Abstract: 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 k-length binary information sequences are mapped to 2k n-length permutation codeword signal points in a n-dimensional modulation constellation ?n. The constellation ?n with the coset characteristics is formed by selecting 2k n-length permutation codewords from n(n?1) permutation codewords of a code set Pn,xi of the (n, n(n?1), n?1) permutation group code based on coset partition. The constellation ?n is a coset code in which 2k1 cosets are included and each coset includes 2k2 permutation codewords, where k=k1+k2, and 2k?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.