Compound precoding: a pre-equalisation technique for the bandlimited Gaussian channel

Compound precoding is a state-of-the-art technique for combining trellis coding and decision-feedback equalisation (DFE) prior to upstream transmission on the telephone-line channel, and is an option in the International Telecommunications Union (ITU)-T V.92 standard. In this paper, we provide a detailed overview of this technique. We demonstrate that compound precoding combines in a straightforward manner with most practical trellis codes. We show that compound precoding exhibits a signal-to-noise ratio (SNR) gain with respect to other schemes which combine with trellis coding, and quantify this gain. We also show that, for stability of the compound precoder, the precoder feedforward filter must be decomposed into its constituent minimum phase (MP) and all pass (AP) components. Finally, a simulation study of V.92 upstream transmission demonstrates the shaping advantage of compound precoding over competitor techniques for pre-equalisation in this setting.