Rate-optimal schedule for multi-rate DSP computations

In this paper we present a novel framework of multi-rate scheduling of signal processing programs represented by regular stream ow graphs (RSFGs). The main contribution of this paper is translating the scheduling problem of RSFGs into an equivalent problem in the domain of Karp-Miller computation graphs. A distinct feature of our scheduling framework | called the multi-rate software pipelining | is to allow maximum overlapping of operations from successive iterations, subject only to precedence constraints caused by data dependences. We demonstrate that the scheduling of regular stream ow graphs can be formulated as a mathematical problem by capturing data dependences between two actors as a precedence relation between the ring of these actors. Using linear schedules, the problem is further translated into a linear program formulation. An eecient solution for the linear programmingproblem is obtained by rst constructing what is called the precedence graph. A polynomial-time solution is obtained by observing that the optimal computation rate is the minimum cost-to-time ratio cycle (MCTRC) in the precedence graph and using the well-established solution methods for the MCTRC problem. Finally, to minimize the buuer requirement for the obtained rate-optimal schedule, a graph coloring method based on the cyclic interval graph representation has been proposed.