Finding Space-Time Transformations for Uniform Recurrences viaBranching Parametric Linear Programming

  • Authors:

  • Karl-Heinz Zimmermann;Wolfgang Achtziger

  • Affiliations:

  • Department of Electrical and Computer Engineering, Technical University of Hamburg-Harburg, 21073 Hamburg, Germany;Department of Applied Mathematics, University of Erlangen-Nuremberg, 91058 Erlangen, Germany

  • Venue:
  • Journal of VLSI Signal Processing Systems
  • Year:
  • 1997

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Abstract

Many important algorithms in signal and image processingcan be described by uniform recurrences. A common method for thesynthesis of systolic arrays from uniform recurrences is based onspace-time transformations each of which consisting of two linearmappings, an allocation and a timing function. In this paper, weaddress the problem of finding space-time transformations which aretime-optimal or at least nearly time-optimal. For a given allocationfunction, a continuous relaxation of this problem is studied bypassing from linear to quasi-linear timing functions. A parametrizedlinear programming formulation is provided for finding quasi-lineartiming functions. The solution of each such linear problem, however,depends on the basis representation of the null space of theallocation function. Therefore, a branching approach is proposed forfinding quasi-linear timing functions which are optimal or have atleast low latency. It will be demonstrated by several large testexamples that branching into hundreds or even thousands of linearsubproblems can be computed with reasonable effort and often leads toan optimum linear timing function.