A differential encoder is developed that preserves the phase trellis of continuous phase frequency shift keying (CPFSK) through differential demodulation. This differential encoder interfaces well with the decomposed model of CPFSK, creating a decomposed model of differentially-encoded and differentially-demodulated CPFSK (DCPFSK). The normalised minimum squared Euclidean distance d2min of uncoded DCPFSK is calculated. A code search model is developed, allowing codes over rings to be specifically designed for DCPFSK. The results of code searches show that there is very little loss in d2min when comparing coded DCPFSK systems with coherently-demodulated coded CPFSK systems. The performance of uncoded and coded DCPFSK systems in both additive white Gaussian noise (AWGN) and Rayleigh flat fading is analysed and simulated. DCPFSK is shown to be relatively robust to medium to slowly-varying fading, without the use of any additional techniques. Rate-1/2 encoded quaternary DCPFSK with modulation index h = 1/4 is compared with coherently-demodulated uncoded MSK and differentially-encoded and differentially- demodulated minimum shift keying (DMSK) without error-control coding, in AWGN and Rayleigh flat fading. The coded system shows that significant performance improvement can be obtained through simple coding, particularly in Rayleigh flat fading.