Exploiting general coefficient representation for the optimal sharing of partial products in MCMs

We propose a new algorithm that maximizes he sharing of partial terms in Multiple Cons an Multiplication (MCM) operations under a general number representation for the coefficients. MCM operations are required by many algorithms in digital signal processing and have been the subject of extensive research. By making no assumptions as to the number representation, the algorithm described in his paper is able to perform a better search for the optimal sharing of partial terms than previous methods based on MSD or CSD representations. We have applied our algorithm for the hardware minimization of FIR filers.The results show that we can ob ain solutions that require between 20% to 50% less hardware when compared agains he solutions using he MSD representation.

[1]  Gian Carlo Cardarilli,et al.  Tradeoffs between residue number system and traditional FIR filters , 2001, ISCAS 2001. The 2001 IEEE International Symposium on Circuits and Systems (Cat. No.01CH37196).

[2]  H. T. Nguyen,et al.  Number-splitting with shift-and-add decomposition for power and hardware optimization in linear DSP synthesis , 2000, IEEE Trans. Very Large Scale Integr. Syst..

[3]  Powers-of-Two Coefficients.  An Improved Search Algorithm for the Design of Multiplierless FIR Filters with , 1989 .

[4]  R. Hartley.  Subexpression sharing in filters using canonic signed digit multipliers , 1996 .

[5]  Hyeong-Ju Kang,et al.  Digital filter synthesis based on minimal signed digit representation , 2001, Proceedings of the 38th Design Automation Conference (IEEE Cat. No.01CH37232).

[6]  Miodrag Potkonjak,et al.  Efficient Substitution of Multiple Constant Multiplications by Shifts and Additions Using Iterative Pairwise Matching , 1994, 31st Design Automation Conference.

[7]  Patrick Schaumont,et al.  A new algorithm for elimination of common subexpressions , 1999, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[8]  A. Dempster,et al.  Use of minimum-adder multiplier blocks in FIR digital filters , 1995 .

[9]  Paulo F. Flores,et al.  Maximal sharing of partial terms in MCM under minimal signed digit representation , 2005, Proceedings of the 2005 European Conference on Circuit Theory and Design, 2005..

[10]  G. Venkatesh,et al.  Techniques for low power realization of FIR filters , 1995, Proceedings of ASP-DAC'95/CHDL'95/VLSI'95 with EDA Technofair.