This paper deals with a receiver scheme where adaptive equalization and channel decoding are jointly optimized in a iterative process. This receiver scheme is well suited for transmissions over a frequency-selective channel with large delay spread and for high spectral efficiency modulations. A low-complexity soft-input soft-output M-ary channel decoder is proposed. Turbo equalization allows intersymbol interference to be reduced drastically. For most time-invariant discrete channels, the turbo-equalizer performance is close to the coded Gaussian channel performance, even for low signal-to-noise ratios. Finally, results over time-varying frequency-selective channel proves the excellent behavior of the turbo equalizer.