Designing Garbage-Free Reversible Implementations of the Integer Cosine Transform

摘要

Discrete linear transformations are important tools in information processing. Many such transforms are injective and therefore prime candidates for a physically reversible implementation into hardware. We present here reversible integer cosine transformations on n input integers. The resulting reversible circuit is able to perform both the forward transform and the inverse transform. The detailed structure of such a reversible design strongly depends on the odd prime factors of the determinant of the transform: whether those are of the form 2(k) +/- 1 or of the form 2(k) +/- 2(l) +/- 1 or neither of these forms.