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Turbo equalisation is a state-of-the-art receiving scheme for coded data transmission over channels introducing intersymbol interference (ISI). The author investigates turbo equalisation performance in the presence of ISI and impulsive noise. The design imperfections contributing to the non-robustness of the standard turbo equaliser to outliers are identified, and a novel turbo equaliser, at almost no additional increase in complexity, is proposed for joint mitigation of ISI and impulsive noise. The proposed turbo equaliser incorporates a Talwar penalty function into the maximum a posteriori (MAP) component equaliser to serve two purposes. First, it improves the estimation of the transition probabilities for all transitions through the trellis and for subsequent determination of the a posteriori log-likelihood ratio. Secondly, it absorbs the outliers and prevents them from spreading into the MAP constituent decoder. Simulation results based on Proakis's channel models show that the proposed turbo equaliser achieves a dramatic improvement over the standard turbo equaliser in impulsive noise. At a bit error rate (BER) of 10-2, the performance gain is as large as 3.5 to 5 dB, and as large as 7 to 8 dB at a BER of 10-3.