Abstract
Given a behavioral description of a DSP algorithm represented by a data-flow graph, we show how to obtain a rate-optimal static schedule with the minimum unfolding factor under two models, integral grid model and fractional grid model, and two kinds of implementations for each model, pipelined implementation and non-pipelined implementation. We present a simple and unified approach to deal with the four possible combinations. A unified polynomial-time scheduling algorithm is presented, which works on the original data-flow graphs without really unfolding. The values of the minimum rate-optimal unfolding factors and the general properties for all the four combinations are proved.
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L.-F. Chao and E.H.-M. Sha, “Retiming and unfolding data-flow graphs,”Proceedings of the International Conference on Parallel Processing, St. Charles, IL, Aug. 1992, pp. II 33–40.
A. Zaky and P. Sadayappan, “Optimal static scheduling of sequential loops on multiprocessors,”Proceedings of the International Conference on Parallel Processing, pp. III 130–137, 1989.
E.A. Lee and D.G. Messerschmitt, “Static scheduling of synchronous data flow programs fordigital signal processing,”IEEE Transactions on Computers, Vol. 36, pp. 24–35, 1987.
S. Shukla, B. Little, and A. Zaky, “A compile-time technique for controlling real-time execution of task-level data-flow graphs,”Proceedings of the International Conference on Parallel Processing, Naval Postgraduate School, pp. II 49–56, Aug. 1992.
M. Renfors and Y. Neuvo, “The maximum sampling rate of digital filters under hardware speed constraints,”IEEE Transactions on Circuits and Systems, Vol. CAS-28, pp. 196–202, 1981.
L.-F. Chao and E.H.-M. Sha, “Unfolding and retiming data-flow DSP programs for RISC multiprocessor scheduling,”Proceedings of the IEEE International Conference on Acoustic, Speech, and Signal Processing, San Francisco, CA, Mar. 1992, pp. V565–V568.
L.-G. Jeng and L.-G. Chen, “A globally static rate optimal scheduling for recursive DSP algorithms,”Proceedings of the IEEE International Conference on Acoustic, Speech, and Signal Processing, pp. 1005–1008, May 1991.
L.-G. Jeng and L.-G. Chen, “Synthesis of rate-optimal DSP algorithms by pipeline and minimum unfolding,”Proceedings of the ACM/IEEE International Workshop on High-Level Synthesis, pp. 159–168, Nov. 1992.
L.E. Lucke, A.P. Brown, and K.K. Parhi, “Unfolding and retiming for high-level DSP synthesis,”Proceedings of the International Symposium on Circuits and Systems, pp. 2351–2354, 1991.
K.K. Parhi and D.G. Messerschmitt, “Static rate-optimal scheduling of iterative data-flow programs via optimum unfolding,”IEEE Transactions on Computers, Vol. 40, pp. 178–195, 1991.
D.J. Wang and Y.H. Hu, “Optimal scheduling of linear recurrence equations on a multi-processor array,”Proceedings of the IEEE International Conference on Acoustic, Speech, and Signal Processing, Toronto, May 1991, pp. 1581–1584.
D.J. Wang and Y.H. Hu, “Fully static multiprocessor realization for real-time recursive DSP algorithms,”International Conference on Application-Specific Array Processors, Aug. 1992, pp. 664–678.
A. Aiken and A. Nicolau, “Optimal loop parallelization,”Proceedings of the ACM SIGPLAN Conference on Programming Languages Design and Implementation, pp. 308–317, June 1988.
G.R. Gao, Y.-B. Wong, and Q. Ning, “A timed petri-net model for fine-grain loop scheduling,”Proceedings of the ACM SIGPLAN Conference on Programming Languages Design and Implementation, pp. 204–218, June 1991.
L.-F. Chao and E.H.-M. Sha, “Efficient retiming and unfolding,”Proceedings of the IEEE International Conference on Acoustic,Speech, and Signal Processing, pp. I 421–424, Apr. 1993.
L.E. Lucke and K.K. Parhi, “Generalized ILP scheduling and allocation for high-level DSP synthesis,”Proceedings of the IEEE Custom Integrated Circuits Conference, pp. 5.4.1–5.4.4, May 1993.
L.-F. Chao, “Scheduling and behavioral transformations for parallel systems,” Ph.D. Thesis, Tech. Rep. CS-TR-430-93, Department of Computer Science, Princeton University, July 1993.
M. Lam, “Software pipelining: An effective scheduling technique for VLIW machines,”Proceedings of the ACM SIGPLAN Conference on Programming Languages Design and Implementation, Atlanta, GA, June 1988, pp. 318–328.
L.-F. Chao and E.H.-M. Sha, “Rate-optimal static scheduling for DSP data-flow programs,”Proceedings of the Great Lakes Symposium on VLSI, Kalamazoo, Michigan, Mar. 1993, pp. 80–84.
R.E. Tarjan,Data Structures and Network Algorithms, Philadelphia, PA: SIAM, 1983.
E.L. Lawler,Combinatorial Optimization: Networks and Matroids, New York: Holt, Rinehart and Winston, 1976.
L.B. Jackson,Digital Filters and Signal Processing, pp. 47–53, Kluwer Academic Publishers, 1986.
J.-G. Chung and K. Parhi, “Design of pipelined lattice IIR digital filters,”Proceedings of the Asilomar Conference on Signals, Systems, and Computers, pp. 1021–1025, Nov. 1991.
R. Camposano and W. Wolf (Eds.),High-Level Synthesis, Boston: Kluwer Academic Publishers, 1991.
G. Goossens, F. Catthoor, D. Lanneer, and H.D. Man, “Integration of signal processing systems on heterogeneous IC architectures,”Proceedings of the ACM/IEEE International Workshop on High-Level Synthesis, Nov. 1992.
K. Iwano and S. Yeh, “An efficient algorithm for optimal loop parallelization,”Proceedings of The First International Symposium of Algorithms, Dec. 1990.
P.R. Gelabert and T.P. Bamwell, “Optimal automatic periodic multiprocessor scheduler for fully specified flow graphs,”IEEE Transactions on Signal Processing, Vol. 41, pp. 858–888, 1993.
N. Passos, E.H.-M. Sha, and S.C. Bass, “Partitioning and retiming of multi-dimensional systems,”Proceedings of the International Symposium on Circuits and Systems, 1994.
N. Passos and E.H.-M. Sha, “Full parallelism in uniform nested loops using multi-dimensional retiming,”Proceedings of the International Conference on Parallel Processing, Aug. 1994.
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The work of Chao was supported in part by DARPA/ONR contract N00014-88-K-0459 and NSF award MIP90-23542 while the author was with Princeton University.
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Chao, LF., Hsing-Mean Sha, E. Static scheduling for synthesis of DSP algorithms on various models. Journal of VLSI Signal Processing 10, 207–223 (1995). https://doi.org/10.1007/BF02120029
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DOI: https://doi.org/10.1007/BF02120029