An analytical approach for dynamic range estimation

ABSTRACT

It has been widely recognized that the dynamic range information of an application can be exploited to reduce the datapath bitwidth of either processors or ASICs, and therefore the overall circuit area, delay and power consumption. While recent proposals of analytical dynamic range estimation methods have shown significant advantages over the traditional profiling-based method in terms of runtime, we argue that the rather simplistic treatment of input correlation may lead to significant error. We instead introduce a new analytical method based on a mathematical tool called Karhunen-Loeve Expansion (KLE), which enables the orthogonal decomposition of random processes. We show that when applied to linear systems, this method can not only lead to much more accurate result than previously possible, thanks to its capability to capture and propagate both spatial and temporal correlation, but also richer information than the value bounds previously produced, which enables the exploration of interesting trade-off between circuit performance and signal-to-noise ratio.

REFERENCES

• 1: Yun Cao , Hiroto Yasuura, A system-level energy minimization approach using datapath width optimization, Proceedings of the 2001 international symposium on Low power electronics and design, p.231-236, August 2001, Huntington Beach, California, United States [doi>10.1145/383082.383142]
• 2: K. Kum and W. Sung. Combined word-length optimization and high-level synthesis of digital signal processing systems. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 20(8):921--930, August 2001.
• 3: Joan Carletta , Robert Veillette , Frederick Krach , Zhengwei Fang, Determining appropriate precisions for signals in fixed-point IIR filters, Proceedings of the 40th conference on Design automation, June 02-06, 2003, Anaheim, CA, USA [doi>10.1145/775832.775998]
• 4: Alberto Garcia-Ortiz , Lukusa Kabulepa , Tudor Murgan , Manfred Glesner, Moment-Based Power Estimation in Very Deep Submicron Technologies, Proceedings of the 2003 IEEE/ACM international conference on Computer-aided design, p.107, November 09-13, 2003 [doi>10.1109/ICCAD.2003.98]
• 5: S. Mahlke, R. Ravindran, M. Schlansker, R. Schreiber, and T. Sherwood. Bitwidth cognizant architecture synthesis of custom hardware accelerators. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 20(11):1355--1371, November 2001.
• 6: Claire Fang Fang , Rob A. Rutenbar , Markus Püschel , Tsuhan Chen, Toward efficient static analysis of finite-precision effects in DSP applications via affine arithmetic modeling, Proceedings of the 40th conference on Design automation, June 02-06, 2003, Anaheim, CA, USA [doi>10.1145/775832.775960]
• 7: A. Papoulis. Probability, Random Variables, and Stochastic Processes. McGraw-Hill, New York, 1984.
• 8: I. T. Jolliffe. Principal Component Analysis. Springer-Verlag, New York, 2002.
• 9: J. E. Kolassa. Series Approximation Methods in Statistics. Springer-Verlag, New York, 1994.
• 10: Robert H. Shumway , David S. Stoffer, Time Series Analysis and Its Applications (Springer Texts in Statistics), Springer-Verlag New York, Inc., Secaucus, NJ, 2005
• 11: Michel C. Jeruchim , Philip Balaban , K. Sam Shanmugan, Simulation of Communication Systems: Modeling, Methodology and Techniques, Kluwer Academic Publishers, Norwell, MA, 2000

INDEX TERMS

Primary Classification:
  B. Hardware
  B.7 INTEGRATED CIRCUITS
      B.7.2 Design Aids

General Terms:
Algorithms, Design, Theory

Keywords:
Karhunen-Loeve Expansion (KLE), bitwidth, correlation, dynamic range