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Two improvements are presented for adaptive equalization of communication channels for data transmission. One of them is designed to mitigate the effects of impulsive noise on the channel through data-adaptive nonlinear filtering. The other improvement uses low-rank approximation techniques to adaptively prefilter the received training waveform which is to be used for adaptive equalization. This permits successful equalization to be carried out with less received data and at lower values of signal-to-noise ratio (SNR).