Exploring Scalable Schedules for IIR Filters

Linear di erence equations involving recurrences are fundamental equations that describe many important signal processes, in particular, in nite-duration impulse response (IIR) lters. Applying conventional dependence-preserving parallelization techniques such as software pipelining can only extract limited parallelismdue to loop-carried dependences in the linear recurrences, and thus cannot achieve scalable speedup given more resources. Furthermore, the previously published scheduling techniques do not have the capability for exploring design space of parallel schedules implementing IIR lters. In this paper, we present a novel approach, based Harmonic Scheduling, that explores design space of scalable parallel schedules implementing IIR lters with resource constraints. The salient features of our approach include a mathematical formulation of the relationship between the schedules, resource constraints and target performance, and capabilities for exploring design space in terms of those parameters. In particular, our approach can be used to successively approximate time-optimal schedules implementing IIR lters for a given target architecture. We illustrate our approach by giving an algorithm for deriving scalable schedules for IIR lters with a xed number of identical multi-functional processors. As a further illustration, we derive rate-optimal schedules for IIR lters under more realistic constraints: using a xed number of adders and multipliers and assuming that multiplication and addition take dissimilar execution times. Index terms|High-(algorithmic-)level synthesis, scheduling with resource constraints, scalable schedules, loop-carried dependence, in nite impulse responce (IIR) lters.