Low complexity coded modulation with codes over Zm

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 Ai-ary phase-shift keying (M-PSK) codes over the ring structure ZM, the ring of integers modulo M, (where M = 4), for code length n ≤ 10. The proposed code Cs offers good squared Euclidean distance d²e with high decoding complexity. Therefore, to apply iterative decoding, the reduced complexity trellis parent code Cp has been investigated and found. The parent code Cp presents about one-fourth of Viterbi decoding complexity compared to Cs, where Cs ⊂ Cp. Depending upon the number of iterations and trellis complexity of the parent codes, there is little performance degradation. Computer simulation of the subcodes Cs, using the trellises of the parent codes Cp, 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 ML soft decision decoding when the decoding is performed by iterative decoding using reduced trellis parent codes.