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This paper presents a new application of a suboptimal trellis decoding algorithm for combined equalization and decoding. The proposed algorithm can outperform the reduced-state sequence estimator (RSSE) of the same order of complexity. The algorithm, termed estimated future decision-feedback algorithm (EFDFA), was originally proposed for the problem of noncoherent decoding with multiple-symbol overlapped observations and is now reformulated for the problem of intersymbol interference inflicted channels. The EFDFA uses the RSSE as a building block. The performance improvement is achieved by using estimated future symbols in the decision process. The estimated future symbols are obtained by RSSE decoding time-reversed blocks of the input. The same technique can be used to greatly enhance the performance of the conventional decision-feedback equalizer. An analysis of the performance of the EFDFA based on the performance of the RSSE is described. The EFDFA can be configured as an adaptive equalizer capable of operating in a time-varying environment, and is shown to perform well in fading conditions. With only minor additional complexity, the EFDFA is also capable of producing soft outputs.