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The performance of many very high bit rate digital subscriber line (VDSL) systems is limited by the effects of crosstalk among the wires in a bundle. For the downstream, a precoder can compensate for this, provided that some crosstalk channel information is available at the transmitter. In this paper, we investigate the issue of precoder design based on a particular type of feedback: it is assumed that each receiver sends back the (complex) sign of the noise on the symbol detection as a way to provide the needed information on crosstalk channels. We derive an algorithm that makes use of this limited information in an adaptive way to iteratively compute the precoder. The performance of the proposed algorithm is extensively analyzed, both with theoretical evaluations and simulation results. The algorithm is also compared to other solutions, showing the efficient performance for the limited amount of overhead it requires.