ALGEBRAIC DECODING METHOD AND DECODER FOR (N,N(N-1),N-1)-PGC IN COMMUNICATION MODULATION SYSTEM

摘要

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.