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We consider the problem of lower bounding the information rate of intersymbol interference channels via Monte Carlo algorithms. We adopt a novel approach based on the Ungerboeck observation model, unlike the existing ones that are all based on the Forney model. The two approaches, yet equivalent in the case of full-complexity detection, lead to different results in the case of reduced-complexity detection, which is the only viable option when the channel memory is large. The proposed approach significantly outperforms the existing ones for all practical values of the signal-to-noise ratio.