Effective channel coding of serially concatenated encoders and CPM over AWGN and Rician channels

A generic M-ary continuous phase modulation (CPM) scheme, with a modulation index of h=1/M, can be modeled by a continuous-phase encoder (CPE) followed by a memoryless modulator (MM), where the CPE is linear over the ring of integers module M. By designing a channel encoder (CE), which is a convolutional encoder, to operate over the same ring of integers module M, the CE and the CPE can be combined to create another convolutional encoder called an extended CE. In this paper, a 1/2 rate CE over the ring of integers modulo 4 is combined with a 4-ary CPM scheme whose modulation index is h= 1/4 . Using this trellis coded modulation design, the paper explains the design of an effective serially concatenated channel coded system, where the inner encoder is the extended CE and the outer encoder is another convolutional encoder. Simulations show that good results are obtainable by concatenating an outer quaternary convolutional encoder with the quaternary extended CE.