Concordant and partially concordant ring convolutional codes for CPFSK

We consider new M-ary convolutional codes over the ring of integers Z/sub M/ for full response continuous phase frequency shift keying (CPFSK) with modulation index h=p/g, where positive integers p and q have no common factors. In comparison with the other best known constructions of encoded CPFSK, our encoder is feedback-free. The new trellis codes are designed for additive white Gaussian noise channels, where in the receiver we carry out Viterbi decoding on the joint trellis of encoded CPFSK. In such a case the decoding complexity is mainly defined by the number of states of joint trellis S, and S/sub c//spl les/S/spl les/S/sub cq/, where S/sub c/ is the number of states in the trellis diagram of the convolutional code and q defines the number of states in the trellis diagram of CPFSK. We show, that there exist convolutional codes for which S=S/sub cq//GCD(M,q). It follows that if GCD(M,q)=q then S=S/sub c/. We call such convolutional codes concordant codes. Then if GCD(M,q)=1 we have S=S/sub cq/ and such codes are non-concordant codes. Finally if 1