Decoupling the dimension of a system of affine recurrence equations

Abstract

Most work on the problem of synthesizing a systolic array from a system of recurrence equations is restricted to systems of uniform recurrence equations. In this paper, this restriction is relaxed to include systems of affine recurrence equations. A system of uniform recurrence equations typically can be embedded in space-time so that the distance between a variable and a dependent variable does not depend on the problem size. Systems of affine recurrence equations which are not uniform do not enjoy this property. However, a method has been presented in another paper for converting a system of affine recurrence equations to an equivalent system of recurrence equations that is uniform, except for points near the boundaries of its index sets. In this paper a procedure is presented for decoupling the dimensions of the system of affine recurrence equations, thereby simplifying the conversion to an equivalent system that is uniform (except for points near the boundaries).