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Exploring scalable schedules for IIR filters with resource constraints

Linear difference equations involving recurrences are fundamental equations that describe many important signal processes; in particular, infinite-duration impulse response (IIR) filters. Applying conventional dependence-preserving parallelization techniques such as software pipelining can only extract limited parallelism due to loop-carried dependences in the linear recurrences, and thus, cannot achieve scalable speedup given more resources. Furthermore, the previously published scheduling techniques did not address the tradeoffs between resource constraints and the processing speed of the resulting schedules, and thus, do not have the capability of exploring the design space of parallel schedules implementing IIR filters. In this paper, we present a novel approach, based on harmonic scheduling, that addresses the tradeoffs between resource constraints and the processing speed of the resulting schedules, which can be used to explore the design space of scalable parallel schedules implementing IIR filters 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 filters for a given target architecture. We illustrate our approach by giving an algorithm for deriving scalable schedules for IIR filters with a fixed number of identical multifunctional processors. As a further illustration, we derive rate-optimal schedules for IIR filters under more realistic constraints: using a fixed number of adders and multipliers and assuming that multiplication and addition take dissimilar execution times.