Area-Effective FIR Filter Design for Multiplier-less Implementation

1. Area-Effective FIR Filter Design for Multiplier-less Implementation Tay-Jyi Lin, Tsung-Hsun Yang, and Chein-Wei Jen Department of Electronics Engineering National Chiao Tung University, Taiwan {tjlin, thyang, cwjen}@twins.ee.nctu.edu.tw

2. In this paper • We propose a complexity-aware quantization algorithm of FIR filters, which enables designers to explicitly trade quantization error for simpler implementations • The proposed algorithm precisely distributes a pre-defined addition budget among the filter coefficients with successive approximation and common subexpression elimination

3. Outline • Preliminary • Quantization by Successive Coefficient Approximation • Common Subexpression Elimination • Complexity-Aware Coefficient Quantization • Simulation Result • Conclusion

4. Quantization by Successive Approximation* * D. Li, Y. C. Lim, Y. Lian, and J. Song, “A polynomial-time algorithm for designing FIR filters with power-of-two coefficients,” IEEE Trans. Signal Processing, vol.50, pp.1935-1941, Aug 2002

5. Constant Multiplications • Consider a 4-tap FIR filter with the coefficients: h0=0.0111011, h1=0.0101110, h2=1.0110011, and h3=0.0100110 Common Subexpression across Coefficients (CSAC)

6. CSAC CSWC Common Subexpression Elimination • Tabular form

7. Steepest-descent CSE Heuristic* * M. Mehendale, S. D. Sherlekar, VLSI Synthesis of DSP Kernels - Algorithmic and Architectural Transformations, Kluwer Academic Publishers, 2001

8. Outline • Preliminary • Complexity-Aware Coefficient Quantization • Simulation Result • Conclusion

9. Complexity-Aware Quantization Complexity-aware allocation of non-zero terms (with CSE) Improved SF Exploration (next page)

10. Improved SF Exploration • Instead of the fixed 2-w stepping from the lower bound, the next SF is calculated as denotes the magnitude of a coefficient denotes the distance to its next quantization level as the SF increases, which depends on the approximation scheme (e.g. rounding to the nearest value, toward 0, or toward -∞, etc).

11. Simulation Result CSE Improved SF Search For 16-bit wordlength and ±3dB acceptable gain, the improved SF exploration has 14,986 to 20,429 candidates depending on the coefficients, instead of 45,875 for all.

12. Conclusion • Successive approximation with appropriate scaling can significantly reduce the addition complexity • The proposed algorithm controls the CSE to incur the minimum additions during the successive approximation • The improved SF exploration finds better or identical (but never worse) results with only 1/3 candidates • The proposed complexity-aware quantization algorithm allows designers to explicitly trade quantization error for simpler implementations, which can also be easily • modified for goals other than small area (e.g. low power, etc), or • adapted to other implementation styles (e.g. FIR code generation for programmable processors)