Levent Aksoy
Paulo Flores
ABSTRACT
The multiple constant multiplications (MCM) problem, that is defined as finding the minimum number of addition and subtraction operations required for the multiplication of multiple constants by an input variable, has been the subject of great interest since the complexity of many digital signal processing (DSP) systems is dominated by an MCM operation. This paper introduces a variant of the MCM problem, called multiple tunable constant multiplications (MTCM) problem, where each constant is not fixed as in the MCM problem, but can be selected from a set of possible constants. We present an exact algorithm that formalizes the MTCM problem as a 0--1 integer linear programming (ILP) problem when constants are defined under a number representation. We also introduce a local search method for the MTCM problem that includes an efficient MCM algorithm. Furthermore, we show that these techniques can be used to solve various optimization problems in finite impulse response (FIR) filter design and we apply them to one of these problems. Experimental results clearly show the efficiency of the proposed methods when compared to prominent algorithms designed for the MCM problem.
- L. Aksoy, E. Costa, P. Flores, and J. Monteiro. Exact and Approximate Algorithms for the Optimization of Area and Delay in Multiple Constant Multiplications. IEEE TCAD, 27(6): 1013--1026, 2008. Google Scholar
Digital Library
- L. Aksoy, E. Gunes, and P. Flores. Search Algorithms for the Multiple Constant Multiplications Problem: Exact and Approximate. Elsevier MICPRO Journal, 34(5): 151--162, 2010. Google ScholarDigital Library
- M. Aktan, A. Yurdakul, and G. Dündar. An Algorithm for the Design of Low-Power Hardware-Efficient FIR Filters. IEEE TCAS, 55(6): 1536--1545, 2008.Google Scholar
- P. Barth. A Davis-Putnam Based Enumeration Algorithm for Linear Pseudo-Boolean Optimization. Technical report, MPII, 1995.Google Scholar
- O. Coudert. On Solving Covering Problems. In DAC, pages 197--202, 1996. Google ScholarDigital Library
- A. Dempster and M. Macleod. Constant Integer Multiplication Using Minimum Adders. IEE Proceedings - Circuits, Devices and Systems, 141(5): 407--413, 1994.Google ScholarCross Ref
- A. Dempster and M. Macleod. Use of Minimum-Adder Multiplier Blocks in FIR Digital Filters. IEEE TCAS-II, 42(9): 569--577, 1995.Google Scholar
- M. Ercegovac and T. Lang. Digital Arithmetic. Morgan Kaufmann, 2003.Google Scholar
- M. B. Gately, M. B. Yeary, and C. Y. Tang. Reduced-Hardware Digital Filter Design via Joint Quantization and Multiple Constant Multiplication Optimization. In ICASSP, pages 4368--4371, 2011.Google ScholarCross Ref
- O. Gustafsson. Lower Bounds for Constant Multiplication Problems. IEEE TCAS-II, 54(11): 974--978, 2007.Google Scholar
- O. Gustafsson and L. Wanhammar. ILP Modelling of the Common Subexpression Sharing Problem. In ICECS, pages 1171--1174, 2002.Google ScholarCross Ref
- R. Hartley. Subexpression Sharing in Filters Using Canonic Signed Digit Multipliers. IEEE TCAS-II, 43(10): 677--688, 1996.Google Scholar
- I.-C. Park and H.-J. Kang. Digital Filter Synthesis Based on Minimal Signed Digit Representation. In DAC, pages 468--473, 2001. Google ScholarDigital Library
- D. Shi and Y. J. Yu. Design of Linear Phase FIR Filters With High Probability of Achieving Minimum Number of Adders. IEEE TCAS, 58(1): 126--136, 2011.Google Scholar
- Y. Voronenko and M. Püschel. Multiplierless Multiple Constant Multiplication. ACM Transactions on Algorithms, 3(2), 2007. Google ScholarDigital Library
Index Terms
- Multiple tunable constant multiplications: algorithms and applications
Recommendations
An approximate algorithm for the multiple constant multiplications problem
SBCCI '08: Proceedings of the 21st annual symposium on Integrated circuits and system designMultiple constant multiplications (MCM) problem that is to obtain the minimum number of addition/subtraction operations required to implement the constant multiplications finds itself and its variants in many applications, such as finite impulse ...
Search algorithms for the multiple constant multiplications problem: Exact and approximate
This article addresses the multiplication of one data sample with multiple constants using addition/subtraction and shift operations, i.e., the multiple constant multiplications (MCM) operation. In the last two decades, many efficient algorithms have ...
Efficient shift-adds design of digit-serial multiple constant multiplications
GLSVLSI '11: Proceedings of the 21st edition of the great lakes symposium on Great lakes symposium on VLSIBit-parallel realization of the multiplication of a variable by a set of constants using only addition, subtraction, and shift operations has been explored extensively over the years as large number of constant multiplications dominate the complexity of ...
Comments