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Two different noise prediction schemes incorporated with the finite length of DFE for mitigating the colored noise in the HDSL transmission are analysed and compared. These noise prediction schemes are the double side forward filter (DSFF) and the additional noise predictor (NP) schemes. The optimal coefficient set of the DSFF and the NP are derived under the minimum mean squared error criterion (MMSE). The numerical examples show that both systems offer almost the same performance gain, in the sense of MMSE, over the system with only single side forward filter. In a system using a detector, however, the DSFF scheme needs only a few extra operations for computing the branch metric, while the NP scheme requires a large amount of extra operations. This is because that the DSFF works outside the detector whereas the NP should be added to each survival path in the detector to avoid the error propagation.