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Garbageless reversible implementation of integer linear transformations

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MicroPower
Abstract
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 digital implementations of different integer transformations on four inputs. The resulting reversible circuit is able to perform both the forward transform and the inverse transform. Which of the two computations that actually is performed, simply depends on the orientation of the circuit when it is inserted in a computer board (if one takes care to provide the encapsulation of symmetrical power supplies). Our analysis indicates that the detailed structure of such a reversible design strongly depends on the prime factors of the determinant of the transform: a determinant equal to a power of 2 leads to an efficient garbage-free design.
Keywords
integer linear transformation, H.264 transform, reversible computation, garbage

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Chicago
Burignat, Stéphane, Kenneth Vermeirsch, Alexis De Vos, and Michael Thomsen. 2012. “Garbageless Reversible Implementation of Integer Linear Transformations.” In 4th Workshop on Reversible Computation : Preliminary Proceedings, ed. Robert Glueck and Tetsuo Yokoyama, 187–197. Copenhagen, Denmark: reversible-computation.org.
APA
Burignat, S., Vermeirsch, K., De Vos, A., & Thomsen, M. (2012). Garbageless reversible implementation of integer linear transformations. In R. Glueck & T. Yokoyama (Eds.), 4th workshop on reversible computation : preliminary proceedings (pp. 187–197). Presented at the 4th workshop on reversible computation, Copenhagen, Denmark: reversible-computation.org.
Vancouver
1.
Burignat S, Vermeirsch K, De Vos A, Thomsen M. Garbageless reversible implementation of integer linear transformations. In: Glueck R, Yokoyama T, editors. 4th workshop on reversible computation : preliminary proceedings. Copenhagen, Denmark: reversible-computation.org; 2012. p. 187–97.
MLA
Burignat, Stéphane, Kenneth Vermeirsch, Alexis De Vos, et al. “Garbageless Reversible Implementation of Integer Linear Transformations.” 4th Workshop on Reversible Computation : Preliminary Proceedings. Ed. Robert Glueck & Tetsuo Yokoyama. Copenhagen, Denmark: reversible-computation.org, 2012. 187–197. Print.
@inproceedings{2957832,
  abstract     = {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 digital implementations of different integer transformations on four inputs. The resulting reversible circuit is able to perform both the forward transform and the inverse transform. Which of the two computations that actually is performed, simply depends on the orientation of the circuit when it is inserted in a computer board (if one takes care to provide the encapsulation of symmetrical power supplies). Our analysis indicates that the detailed structure of such a reversible design strongly depends on the prime factors of the determinant of the transform: a determinant equal to a power of 2 leads to an efficient garbage-free design.},
  author       = {Burignat, St{\'e}phane and Vermeirsch, Kenneth and De Vos, Alexis and Thomsen, Michael},
  booktitle    = {4th workshop on reversible computation : preliminary proceedings},
  editor       = {Glueck, Robert and Yokoyama, Tetsuo},
  keyword      = {integer linear transformation,H.264 transform,reversible computation,garbage},
  language     = {eng},
  location     = {Copenhagen, Denmark},
  pages        = {187--197},
  publisher    = {reversible-computation.org},
  title        = {Garbageless reversible implementation of integer linear transformations},
  year         = {2012},
}