Concordant and partially concordant ring convolutional codes forCPFSK

摘要

We consider new M-ary convolutional codes over the ring ofintegers Z_M for full response continuous phase frequencyshift keying (CPFSK) with modulation index h=p/g, where positiveintegers p and q have no common factors. In comparison with the otherbest known constructions of encoded CPFSK, our encoder is feedback-free.The new trellis codes are designed for additive white Gaussian noisechannels, where in the receiver we carry out Viterbi decoding on thejoint trellis of encoded CPFSK. In such a case the decoding complexityis mainly defined by the number of states of joint trellis S, andS_c⩽S⩽S_cq, where S_c is thenumber of states in the trellis diagram of the convolutional code and qdefines the number of states in the trellis diagram of CPFSK. We show,that there exist convolutional codes for whichS=S_cq/GCD(M,q). It follows that if GCD(M,q)=q then S=S_c. We call such convolutional codes concordant codes. Then ifGCD(M,q)=1 we have S=S_cq and such codes are non-concordantcodes. Finally if 1ccq) and we call such convolutional codes partially concordant codes