Comparison between Soft and Hard Decision Decoding using Quaternary Convolutional Encoders and the Decomposed CPM Model

A generic M-ary continuous phase modulation (CPM) scheme, with a modulation index of h = 1/M, can be decomposed into a continuous-phase encoder (CPE) followed by a memoryless modulator (MM), where the CPE is linear over the ring of integers modulo M. By using a channel encoder (CE), which is a convolutional encoder, to operate over the same ring of integers modulo M, the CE and the CPE can be combined to create another convolutional encoder called an extended CE, so called, as the CPE is now an extension of the CE. In this paper, a 1⁄2 rate CE over the ring of integers modulo 4 is combined with the CPE of a quaternary CPM scheme whose modulation index h = 1⁄4. Using this trellis coded modulation design, the paper compares the performance of soft and hard decision decoding of a serially concatenated channel coded system, where the inner encoder is the quaternary extended CE and the outer encoder is another quaternary convolutional encoder. Although simulations show the superiority of soft decision decoding, good results were obtainable from hard decision decoding.