Optimizing the capacity of orthogonal and biorthogonal DMT channels

The uniform DFT filter bank has been used routinely in discrete multitone modulation (DMT) systems because of implementation efficiency. It has recently been shown that principal component filter banks (PCFB) which are known to be optimal for data compression and denoising applications, are also optimal for a number of criteria in DMT communication. In this paper we show that such filter banks are optimal even when scalar prefilters and postfilters are used around the channel. We show that the theoretically optimum scalar prefilter is the half-whitening solution, well known in data compression theory. We conclude with the observation that the PCFB continues to be optimal for the maximization of theoretical capacity as well.