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Design of an RNS reverse converter for a new five-moduli special set

Published: 03 May 2012 Publication History

Abstract

In this paper, we present a new residue number system (RNS) {2n-1, 2n, 2n+1, 2n+1+1, 2n-1+1} of five well-balanced moduli that are co-prime for odd n. This new RNS complements the 5-moduli RNS system proposed before for even n {2n-1, 2n, 2n+1, 2n+1-1, 2n-1-1}. With the new set, we also present a novel approach to designing multi-moduli reverse converters that focuses strongly on critical path analysis and aims at strongly on moving a significant amount of computations off the critical path. The synthesis of the resulting design over the ST Microelectronics 65nm LP library demonstrates that the delay, area, and power characteristics improve the performance and power consumption of the existing complementary 5-moduli set.

References

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P. Ananda Mohan and A. Premkumar. RNS-to-binary converters for two four-moduli sets {2n - 1,2n, 2n + 1, 2n+1 - 1} and {2n - 1, 2n, 2n +1, 2n+1 +1}. IEEE Trans. Circuits Syst. I, 54(6):1245--1254, June 2007.
[2]
B. Cao, C.-H. Chang, and T. Srikanthan. New efficient residue-to-binary converters for 4-moduli set {2n - 1,2n,2n +1,2n+1 - 1}. In Proc. ISCAS, volume 4, pages IV536--IV539, 2003.
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B. Cao, C.-H. Chang, and T. Srikanthan. A residue-to-binary converter for a new five-moduli set. IEEE Trans. Circuits Syst. I, 54(5):1041--1049, May 2007.
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A. Dhurkadas. Comments on a high speed realization of a residue to binary number system converter. IEEE Trans. Circuits Syst. II, 45(3):446--447, Mar. 1998.
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M. Esmaeildoust, K. Navi, and M. Taheri. High speed reverse converter for new five-moduli set {2n,22n+1 - 1,2n/2 - 1,2n/2 + 1,2n + 1}. IEICE Electron. Expr., 7(3):118--125, 2010.
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A. Molahosseini, C. Dadkhah, and K. Navi. A new five-moduli set for efficient hardware implementation of the reverse converter. IEICE Electron. Expr., 6(14):1006--1012, 2009.
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A. Omondi and B. Premkumar. Residue Number Systems: Theory and Implementation. Imperial College Press, London, UK, 2007.
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S. J. Piestrak. High-speed realization of a residue to binary number system converter. IEEE Trans. Circuits Syst. II, 42(10):661--663, Oct. 1995.
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T. Shahana, R. James, B. Jose, K. Jacob, and S. Sasi. Performance analysis of FIR digital filter design: RNS versus traditional. In Proc. Int. Symp. Commun. & Inf. Techn., pages 1--5, 17-19 Oct. 2007.
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T. Toivonen and J. Heikkila. Video filtering with Fermat number theoretic transforms using residue number system. IEEE Trans. Circuits Syst. Video Technol., 16(1):92--101, Jan. 2006.

Cited By

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  • (2024)Balanced Modular Addition for the Moduli Set $\{2^{q},2^{q}\bar{+}1,2^{2q}+1\}$ via Moduli-($(2^{q}\,\bar{+}\,\sqrt{-1})$) AddersIEEE Transactions on Computers10.1109/TC.2024.3461235(1-8)Online publication date: 2024
  • (2018)Design of RNS Reverse Converters with Constant Shifting to Residue Datapath ChannelsJournal of Signal Processing Systems10.1007/s11265-017-1238-690:3(323-339)Online publication date: 1-Mar-2018
  • (2017)Design of Reverse Converters for a New Flexible RNS Five-Moduli Set $$\{ 2^k, 2^n-1, 2^n+1, 2^{n+1}-1, 2^{n-1}-1 \}$${2k,2n-1,2n+1,2n+1-1,2n-1-1} (n Even)Circuits, Systems, and Signal Processing10.1007/s00034-017-0530-936:11(4593-4614)Online publication date: 1-Nov-2017
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  1. Design of an RNS reverse converter for a new five-moduli special set

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      cover image ACM Conferences
      GLSVLSI '12: Proceedings of the great lakes symposium on VLSI
      May 2012
      388 pages
      ISBN:9781450312448
      DOI:10.1145/2206781
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      Published: 03 May 2012

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      Author Tags

      1. 5-moduli set
      2. residue number system
      3. reverse converter

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      May 3 - 4, 2012
      Utah, Salt Lake City, USA

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      View all
      • (2024)Balanced Modular Addition for the Moduli Set $\{2^{q},2^{q}\bar{+}1,2^{2q}+1\}$ via Moduli-($(2^{q}\,\bar{+}\,\sqrt{-1})$) AddersIEEE Transactions on Computers10.1109/TC.2024.3461235(1-8)Online publication date: 2024
      • (2018)Design of RNS Reverse Converters with Constant Shifting to Residue Datapath ChannelsJournal of Signal Processing Systems10.1007/s11265-017-1238-690:3(323-339)Online publication date: 1-Mar-2018
      • (2017)Design of Reverse Converters for a New Flexible RNS Five-Moduli Set $$\{ 2^k, 2^n-1, 2^n+1, 2^{n+1}-1, 2^{n-1}-1 \}$${2k,2n-1,2n+1,2n+1-1,2n-1-1} (n Even)Circuits, Systems, and Signal Processing10.1007/s00034-017-0530-936:11(4593-4614)Online publication date: 1-Nov-2017
      • (2014)Design of Reverse Converters for the New RNS Moduli Set $\{2^{n}+1,2^{n}-1,2^{n},2^{n-1}+1\}$ ($n$ odd)IEEE Transactions on Circuits and Systems I: Regular Papers10.1109/TCSI.2014.233723761:12(3436-3449)Online publication date: Dec-2014
      • (2014)Design of Reverse Converters for General RNS Moduli Sets $\{ 2^{k}, 2^{n}-1, 2^{n}+1, 2^{n+1}-1 \}$ and $\{ 2^{k}, 2^{n}-1, 2^{n}+1, 2^{n-1}-1 \}$ ($n$ even)IEEE Transactions on Circuits and Systems I: Regular Papers10.1109/TCSI.2013.229084361:6(1687-1700)Online publication date: Jun-2014
      • (2012)Research challenges in next-generation residue number system architectures2012 7th International Conference on Computer Science & Education (ICCSE)10.1109/ICCSE.2012.6295382(1658-1661)Online publication date: Jul-2012

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