This project considers the problem of decreasing the probability of error of M-ary continuous-phase modulation (CPM) schemes by means of channel coding. It is argued that the usual technique involving an external binary convolutional encoder is unnatural, and it exploits only part of the coding gain. This project is based on a new solution, which aims to obtain a larger coding gain for the same decoding complexity. The method is by means of M-ary convolutional channel encoders (CE) that explicitly use the state information of the CPM scheme that they feed. The ability to use this method lies in the model for CPM, which consists of a linear sequential circuit denoted continuous-phase encoder (CPE) followed by a memoryless modulator (MM). Since the CPE is M-ary, one can feed-back the content of its memory units and use it explicitly in the CE which is also M-ary and linear over the ring of integers modulo M. Thus the CE has its own memory units and those shared with the CPE. This symbiosis increases the constraint length of the CE without increasing the overall number of states. Codes that are more powerful than the usual ones are obtained without increasing the decoding complexity. Moreover, this solution is not constrained to CPM schemes whose input alphabet's size M is a power of 2. The research on ring codes is of interest in its own. Various recent results are a clear indication that ring and group codes are of great importance for nonbinary modulation schemes.
