Static rate-optimal scheduling of iterative data-flow programs via optimum unfolding

Rate-optimal compile-time multiprocessor scheduling of iterative dataflow programs suitable for real-time signal processing applications is discussed. It is shown that recursions or loops in the programs lead to an inherent lower bound on the achievable iteration period, referred to as the iteration bound. A multiprocessor schedule is rate-optimal if the iteration period equals the iteration bound. Systematic unfolding of iterative dataflow programs is proposed, and properties of unfolded dataflow programs are studied. Unfolding increases the number of tasks in a program, unravels the hidden concurrently in iterative dataflow programs, and can reduce the iteration period. A special class of iterative dataflow programs, referred to as perfect-rate programs, is introduced. Each loop in these programs has a single register. Perfect-rate programs can always be scheduled rate optimally (requiring no retiming or unfolding transformation). It is also shown that unfolding any program by an optimum unfolding factor transforms any arbitrary program to an equivalent perfect-rate program, which can then be scheduled rate optimally. This optimum unfolding factor for any arbitrary program is the least common multiple of the number of registers (or delays) in all loops and is independent of the node execution times. An upper bound on the number of processors for rate-optimal scheduling is given