The use of a multi-track format in both optical and magnetic data storage applications provides for a number of improvements to system performance including data density and data transfer rates. However, the full advantage in data density can only be achieved through the use of joint equalization and joint detection. The complexity of implementation of these functions arc addressed with a transform domain equalization architecture and a reduced complexity detection method based on a breadth first search of a time-varying trellis. The trellis results from a one dimensional representation of a two dimensional target response, obtained by arranging samples from adjacent tracks in a sequence that respects the original proximity of the samples.