research-article

A new balanced 4-moduli set {2^k, 2ⁿ - 1, 2ⁿ + 1, 2ⁿ⁺¹-1} and its reverse converter design for efficient fir filter implementation

Authors:

Gayathri Chalivendra,

Vinay Hanumaiah,

Sarma VrudhulaAuthors Info & Claims

GLSVLSI '11: Proceedings of the 21st edition of the great lakes symposium on Great lakes symposium on VLSI

Pages 139 - 144

https://doi.org/10.1145/1973009.1973038

Published: 02 May 2011 Publication History

Abstract

This paper presents a new four moduli residue number system of the form {2^k, 2ⁿ-1, 2ⁿ⁺¹-1}, n d k d 2n, which is an enhancement of the popular four-moduli set {2ⁿ,2ⁿ-1,2ⁿ,2ⁿ⁺¹-1} (for even n). Our k-mod4 moduli set achieves a higher dynamic range and a better balancing of the binary channels. Using the proposed k-mod4 moduli set helps in reducing the hardware complexity of arithmetic circuits compared with other four-moduli sets for the same performance. Additionally, we provide a reverse converter design, whose hardware complexity and performance are shown to be better than the existing reverse converters for the same dynamic range. Experimental results comparing RNS multiply and accumulate units implemented using the proposed four-moduli set with the state-of-the-art balanced four-moduli sets, show large improvements in area (46%) and power (43%) reduction for various dynamic ranges. This makes our k-mod4 moduli set ideal for digital filters implementation.

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Cited By

Patronik PPiestrak S(2023)Design of reverse converters for the general RNS 3-moduli set {2k, 2n − 1, 2n + 1}EURASIP Journal on Advances in Signal Processing10.1186/s13634-023-01037-82023:1Online publication date: 4-Sep-2023
https://doi.org/10.1186/s13634-023-01037-8
Latha MRachh RMohan P(2023)Residue to binary converter for the extended four moduli set {2k, 2n−1, 2n+1, 2n+1+1} for n oddSādhanā10.1007/s12046-023-02118-y48:2Online publication date: 15-Apr-2023
https://doi.org/10.1007/s12046-023-02118-y
Ananda Mohan P(2018)Reverse Converters for the Moduli Set {$$2^{n}, 2^{n-1}-1,2^{n}-1, 2^{n+1}-1\}(n\,\hbox {Even})$$2n,2n-1-1,2n-1,2n+1-1}(nEven)Circuits, Systems, and Signal Processing10.1007/s00034-017-0725-037:8(3605-3634)Online publication date: 1-Aug-2018
https://dl.acm.org/doi/10.1007/s00034-017-0725-0
Show More Cited By

Index Terms

A new balanced 4-moduli set {2^k, 2ⁿ - 1, 2ⁿ + 1, 2ⁿ⁺¹-1} and its reverse converter design for efficient fir filter implementation
1. Hardware
  1. Integrated circuits
    1. Logic circuits
      1. Arithmetic and datapath circuits

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Efficient reverse converter designs for the new 4-moduli sets {2ⁿ - 1, 2ⁿ, 2ⁿ + 1, 2²ⁿ⁺¹ - 1} and {2ⁿ - 1, 2ⁿ + 1, 2²ⁿ, 2²ⁿ + 1} based on new CRTs

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cover image ACM Conferences

GLSVLSI '11: Proceedings of the 21st edition of the great lakes symposium on Great lakes symposium on VLSI

May 2011

496 pages

ISBN:9781450306676

DOI:10.1145/1973009

General Chairs:
David Atienza
EPFL, Switzerland
,
Yuan Xie
Penn State University, USA
,
Program Chairs:
Jose L. Ayala
Federal University of Pernambuco, Brazil
,
Ken Stevens
University of Utah, USA

Copyright © 2011 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Published: 02 May 2011

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GLSVLSI '11: Great Lakes Symposium on VLSI 2011

May 2 - 4, 2011

Lausanne, Switzerland

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Overall Acceptance Rate 312 of 1,156 submissions, 27%

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Cited By

Patronik PPiestrak S(2023)Design of reverse converters for the general RNS 3-moduli set {2k, 2n − 1, 2n + 1}EURASIP Journal on Advances in Signal Processing10.1186/s13634-023-01037-82023:1Online publication date: 4-Sep-2023
https://doi.org/10.1186/s13634-023-01037-8
Latha MRachh RMohan P(2023)Residue to binary converter for the extended four moduli set {2k, 2n−1, 2n+1, 2n+1+1} for n oddSādhanā10.1007/s12046-023-02118-y48:2Online publication date: 15-Apr-2023
https://doi.org/10.1007/s12046-023-02118-y
Ananda Mohan P(2018)Reverse Converters for the Moduli Set {$$2^{n}, 2^{n-1}-1,2^{n}-1, 2^{n+1}-1\}(n\,\hbox {Even})$$2n,2n-1-1,2n-1,2n+1-1}(nEven)Circuits, Systems, and Signal Processing10.1007/s00034-017-0725-037:8(3605-3634)Online publication date: 1-Aug-2018
https://dl.acm.org/doi/10.1007/s00034-017-0725-0
Patronik PPiestrak S(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
https://dl.acm.org/doi/10.1007/s00034-017-0530-9
Ananda Mohan PMohan P(2016)RNS to Binary ConversionResidue Number Systems10.1007/978-3-319-41385-3_5(81-132)Online publication date: 15-Oct-2016
https://doi.org/10.1007/978-3-319-41385-3_5
Vassalos EBakalis D(2015) Efficient architectures for modulo 2 n − 2 arithmetic units International Journal of Electronics10.1080/00207217.2015.1020528102:12(2062-2074)Online publication date: 10-Mar-2015
https://doi.org/10.1080/00207217.2015.1020528
Jaberipur GAhmadifar H(2014) A ROM‐less reverse RNS converter for moduli set {2 q ± 1, 2 q ± 3} IET Computers & Digital Techniques10.1049/iet-cdt.2012.01488:1(11-22)Online publication date: Jan-2014
https://doi.org/10.1049/iet-cdt.2012.0148
SHEU MKUO YLIN SSIAO S(2013)Efficient Reverse Converter Design for New Adaptable Four-Moduli Set {2n+k, 2n + 1, 2n - 1, 22n + 1}IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences10.1587/transfun.E96.A.1571E96.A:7(1571-1578)Online publication date: 2013
https://doi.org/10.1587/transfun.E96.A.1571

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