<title>Theoretical constraints on multidimensional retiming design techniques</title>

Abstract

Image signal processing depends on computation intensive programs, which include the repetition of sequences of operations coded as nested loops. An effective technique in increasing the computing performance of such applications is the design and use of Application Specific Integrated Circuits using loop transformation techniques, and in particular, multidimensional (MD) retiming. The MD-retiming method improves the instruction-level parallelism of uniform loops. While many have written about the multi-dimensional retiming technique, no results have been published on the possible limitations of its application. This paper presents an analysis of that technique and its constraints when applied to nested loops with known index bounds, such as those found in two and three dimensional image processing.