Advertisement

Multiplierless Synthesis of Multiple Constant Multiplications Using Common Subexpression Sharing With Genetic Algorithm

  • Yuen-Hong Alvin Ho
  • Chi-Un Lei
  • Ngai Wong
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 4)

In the context of multiple constant multiplications (MCM) design, we propose a novel common subexpression elimination (CSE) algorithm that models synthesis of coefficients into an estimated cost function. Although the proposed algorithm generally does not guarantee an optimum solution, it is capable of finding the minimum/ minima of the function in practically sized problems. In our design examples that have known optimal solutions, syntheses of coefficients using the proposed method match the optimal results in a defined search space. We also discover the relationship and propose an improvement search space for optimization that combines all minimal signed digit (MSD) representations, as well as the shifted sum (difference) of coefficients to explore the hidden relationship. In some cases, the proposed feasible solution space further reduces the number of adders/subtractors in the synthesis of MCM from all MSD representations.

Keywords

Genetic Algorithm Search Space Critical Path Lookup Table Crossover Operation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Hartley RI (1996) Subexpression sharing in filters using canonic signed digit multipliers. IEEE Trans. Circuits Syst. II 43(10):677–688, Oct.CrossRefGoogle Scholar
  2. 2.
    Park I-C and Kang H-J (2002) Digital filter synthesis based on an algorithm to generate all minimal signed digit representations. IEEE Trans. Computer-Aided Design 21(12): 1525–1529, Dec.CrossRefMathSciNetGoogle Scholar
  3. 3.
    Dempster AG and Macleod MD (2004) Digital filter design using subexpression eliminiation and all signed-digit representations. In Proc. IEEE Int. Symp. on Circuits and Systems 3: III 169–III 172, May 23–26Google Scholar
  4. 4.
    Yao C-Y, Chen H-H, Lin T-F, Chien C-J and Hsu C-T (2004) A novel common-subexpression-elimination method for synthesizing fixed-point FIR filters. IEEE Trans. Circuits Syst. I, 51(11):2215–2221, Nov.CrossRefGoogle Scholar
  5. 5.
    Macleod MD and Dempster AG (2005) Multiplierless FIR filter design algorithms. IEEE Signal Processing Lett. 12(3):186–189, Mar.CrossRefGoogle Scholar
  6. 6.
    Wang Y and Roy K (2005) CSDC: A new complexity reduction technique for multiplierless implementation of digital FIR filters. IEEE Trans. Circuits Syst. I, 52(9):1845–1853, Sept.CrossRefGoogle Scholar
  7. 7.
    Flores P, Monteiro J and Costa E (2005) An exact algorithm for the maximal sharing of partial terms in multiple constant multiplications. In Proc. IEEE Intl. Conf. Computer-Aided Design, San Jose, CA, pp. 13–16, Nov. 6–10Google Scholar
  8. 8.
    Mazumder P and Rudnick EM (1999) Genetic algorithms for VLSI design, layout & test automation.Upper Saddle River, NJ: Prentice-HallGoogle Scholar
  9. 9.
    Gen M and Cheng R (1997) Genetic algorithms and engineering design, Parsaei HR, Ed. New York, NY: John Wiley & SonsGoogle Scholar
  10. 10.
    Bull DR and Horrocks DH (1991) Primitive operator digital filters. Proc. Inst. Elec. Eng. G: Circuits, Devices, Syst. 138(3):401–412Google Scholar
  11. 11.
    Aksoy L, Flores P, Monteiro J, and Costa E (2007) Optimization of area in digital fir filters using gate-level metrics. In Proc. IEEE Design Automation Conference (DAC), San Diego, CA, June 4–8Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  • Yuen-Hong Alvin Ho
    • 1
  • Chi-Un Lei
    • 1
  • Ngai Wong
    • 1
  1. 1.Department of Electrical and Electronic EngineeringThe University of Hong KongChina

Personalised recommendations