Abstract
The Residue Number System (RNS) is a non-weighted number system. Because of its inherent parallelism, it has been extensively studied and used in Digital Signal Processing (DSP) systems. A key arithmetic operation in residue-based real-time computing system is modulo multiplication. For small moduli, ROM-based structures are better at realizing multipliers. Implementations with arithmetic components are more for medium and large moduli due to the exponential growth of ROM sizes. The new modular multiplier introduced in this paper is capable of easily handling medium and large moduli. The multiplier unit is proposed in this paper using shift and add, followed by the modulo operation. The implementation results show that our proposed design outperforms existing architectures in terms of area and power consumption when using the TSMC-180 nm CMOS Technology. When compared to existing works, our proposed multiplier saves 86% to 93% of area and 65% to 83% of power. The proposed multiplier improves the existing DCT architecture by 18% in terms of area.
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References
Shibu M (2007) Modulo adders, multipliers and shared-moduli architectures for moduli of type
Chaves R, Sousa L (2007) Improving residue number system multiplication with more balanced moduli sets and enhanced modular arithmetic structures. IET Comput Digital Tech 1(5):472–480
Hiasat AA (2000) New efficient structure for a modular multiplier for RNS. IEEE Trans Comput 49(2):170–174
Patronik P, Piestrak SJ (2017) Hardware/Software Approach to Designing Low-Power RNS-Enhanced Arithmetic Units. IEEE Trans Circuits Syst I Regul Pap 64(5):1031–1039
Hiasat A (2018) Sign detector for the extended four-moduli set{2n-1,2n+1,22n+1,2n+k}. IET Comput Digital Tech 12(2):39–43
Efstathiou C,Vergos HT, Dimitrakopoulos G, Nikolos D (2005) Efficient diminished-1 modulo 2n+1 multipliers, IEEE Transactions on Computers, 54(4), pp 491–496
Chen JW, Yao RH, and Wu WJ, Efficient Modulo 2n + 1 Multipliers, IEEE Transactions on Very Large Scale Integration (VLSI) Systems
Zimmermann R, “Efficient VLSI implementation of modulo 2n±1 addition and multiplication. In Proceedings 14th IEEE Symposium on Computer Arithmetic (Cat. No.99CB36336), 4, pp 158–167
Soderstrand M, Vernia C (1980) A High-Speed Low-Cost Modulo Pi Multiplier with RNS Arithmetic Application. Proc IEEE 68:529–532
Jullien GA (1980) Implementation of Multiplication, Modulo a Prime Number, with Applications to Theoretic Transforms. IEEE Trans Computers 29(10):899–905
Radhakrishnan D, Yuan Y (1992) Novel Approaches to the Design of VLSI RNS Multipliers, IEEE Trans. Circuits and Systems-II: Analog and Digital Signal Processing 39:52–57
Dugdale M (1994) Residue Multipliers Using Factored Decomposition", IEEE Trans. Circuits and Systems-II: Analog and Digital Signal Processing 41:623–627
Vinogradov IM (1955) An Introduction to the Theory of Numbers. Pergamon Press, New York
Di Claudio E, Piazza F, Orlandi G (May1995) Fast Combinatorial RNS Processors for DSP Applications. IEEE Trans. Computers 44(5):624–633
Sze V, Budagavi M, GJS. Editors (2014) High Efficiency Video Coding (HEVC). Cham: Springer International Publishing
Mohan PVA (2007) RNS-to-binary converter for a new three-moduli set {2n-1, 2n, 2n+1–1}. IEEE Trans. Circuits Syst. II, Exp. Briefs, 54(9), pp 775–779
Singhadia A, Bante P, Chakrabarti I (2019) A Novel Algorithmic Approach for Efficient Realization of 2-DCT Architecture for HEVC. IEEE Trans Consum Electron 65(3):264–273
Acknowledgements
This manuscript is the outcome of the research work carried out at National Institute of Technology Calicut and was supported by Ministry of Education, India.
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Kopperundevi, P., Prakash, M.S. (2024). Multiplier Design for the Modulo Set \(\left\{ {2^{n} - 1,2^{n} ,2^{n + 1} - 1} \right\}\) and Its Application in DCT for HEVC. In: Kalya, S., Kulkarni, M., Bhat, S. (eds) Advances in VLSI, Signal Processing, Power Electronics, IoT, Communication and Embedded Systems. VSPICE 2022. Lecture Notes in Electrical Engineering, vol 1062. Springer, Singapore. https://doi.org/10.1007/978-981-99-4444-6_3
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DOI: https://doi.org/10.1007/978-981-99-4444-6_3
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