Designing Garbage-Free Reversible Implementations of the Integer Cosine Transform
Alexis De Vos, Stéphane Burignat, Robert Glück, Torben Ægidius Mogensen, Holger Bock Axelsen, Michael Kirkedal Thomsen, Eva Rotenberg, Tetsuo Yokoyama · ACM Journal on Emerging Technologies in Computing Systems · 2014
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.