Low complexity coded modulation with codes over Z(M)
Decoding complexity is an important criterion for selecting good modulation codes for the Gaussian channels. In iterative decoding algorithm, lower complexity trellis is used to decode higher complexity trellis and syndrome computation is performed to iteratively search the actual codewords. In this paper, the iterative decoding is applied to our proposed M-ary phase-shift keying (M-PSK) codes over the ring structure Z(M), the ring of integers module M, (where M = 4), for code length eta less than or equal to 10. The proposed code C-s offers good squared Euclidean distance d(e)(2) with high decoding complexity, Therefore, to apply iterative decoding, the reduced complexity trellis parent code C-p has been investigated and found, The parent code C-p presents about one-fourth of Viterbi decoding complexity compared to C-s where C-s subset of C-p. Depending upon the number of iterations and trellis complexity of the parent codes, there is little performance degradation. Computer simulation of the subcodes C-s, using the trellises of the parent codes C-p, provides almost the same error performance compared to conventional maximum-likelihood (ML) decoding when iteration reaches more than 20, The proposed codes present substantial reduction of computational complexity compared to the hit soft decision decoding when the decoding is performed by iterative decoding using reduced trellis parent codes.
coded modulation iterative decoding phase-shift keying ring codes coset codes