Colavolpe and Raheli have proposed (see Proc. IEEE Intern. Conf. Univ. Pers. Commun. (ICUPC'98), Florence, Italy, October 1998, and Proc. Global Commun. Conf., (GLOBECOM'98), Sydney, Australia, 1998), noncoherent sequence detection schemes for any coded modulation. These schemes produce hard decisions via a Viterbi algorithm. The current trend in digital transmission systems toward iterative decoding algorithms motivates an extension of these schemes. We propose a noncoherent soft-output algorithm for coded linear modulations whose structure is similar to that of the well-known algorithm by Bahl et al. (1974). The application to the case of combined detection and decoding of differential or convolutional codes is considered and comparisons with noncoherent sequence detection are performed. As an example of application to iterative processing, noncoherent decoding of turbo codes is considered.