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Practical communication systems often involve frequency selective linear channels and high efficiency amplifiers that exhibits memoryless nonlinearity. In this paper we present a new Gibbs sampling method for the equalization and estimation of data communication signals under a nonlinearity in frequency selective channels. A channel model is developed for an unknown finite impulse response (FIR) distortion under a known nonlinearity. In order to mitigate the effects of the nonlinearity, an improved method for drawing samples from the unknown channel response is presented. This method is shown to closely match the MAP performance of a linear system with the same channel.