Two-dimensional retiming

Tracy C. Denk, Keshab K Parhi

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

This paper considers two-dimensional (2-D) retiming, which is the problem of retiming circuits that operate on 2-D signals. We begin by discussing two types of parallelism available in 2-D data processing, which we call inter-iteration parallelism and inter-operation parallelism. We then present two novel techniques for 2-D retiming that can be used to extract inter-operation parallelism. These two techniques are designed to minimize the amount of memory required to implement a 2-D data-flow graph while maintaining a desired clock rate for the circuit. The first technique is based on an integer linear programming (ILP) formulation of the problem, and is called ILP 2-D retiming. This technique considers the entire 2-D retiming problem as a whole, but long central processing unit times are required if the circuit is large. The second technique, called orthogonal 2-D retiming, is a linear programming formulation which is derived by partitioning ILP 2-D retiming into two parts called s- and a-retiming. This technique finds a solution in polynomial time and is much faster than the ILP 2-D retiming technique, but the two sub-problems (s- and a-retiming) can give results which are not compatible with one another. To solve this incompatibility problem, a variation of orthogonal 2-D retiming called integer orthogonal 2-D retiming is developed. This technique runs in polynomial time and the s-retiming and a-retiming steps are guaranteed to give compatible results. We show that the techniques presented in this paper can result in memory hardware savings of 50% compared to previously published 2-D retiming techniques.

Original languageEnglish (US)
Pages (from-to)198-211
Number of pages14
JournalIEEE Transactions on Very Large Scale Integration (VLSI) Systems
Volume7
Issue number2
DOIs
StatePublished - Jan 1 1999

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Linear programming
Networks (circuits)
Sand
Polynomials
Data flow graphs
Data storage equipment
Computer hardware
Program processors
Clocks

Cite this

Two-dimensional retiming. / Denk, Tracy C.; Parhi, Keshab K.

In: IEEE Transactions on Very Large Scale Integration (VLSI) Systems, Vol. 7, No. 2, 01.01.1999, p. 198-211.

Research output: Contribution to journalArticle

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