Trellis coded modulation with two or multidimensional signal constellations together with coherent maximumlikelihood detection is considered an attractive solution for communications over the additive white Gaussian noise (AWGN) channel. In this paper a new noncoherent communication system is introduced called noncoherent coded modulation (NCM) as an alternative to coherent coded modulation. NCM achieves almost the same power efficiency without bandwidth expansion or an extensive increase in complexity. As a noncoherent system the method does not need carrier phase estimation. Nonetheless differential encoding is not required. High performance noncoherent detection is achieved by using multiple symbol observations. Unlike previous approaches a sliding window for the observations is used with each observation covering several branches of the trellis such that the observations are time-overlapped. We define a new type of noncoherent maximum-likelihood sequence estimator (MLSE) and analyze its performance over the AWGN channel by numerical calculation of the union bound. We perform a computerized search and present new codes for noncoherent detection with their performance. The new codes cover many useful rates and complexities and achieve higher performance than existing codes for noncoherent detection. The method can also be used for multiple symbol demodulation of MDPSK with better results than existing methods.