The Comeback of Reed Solomon Codes

Nir Drucker; Shay Gueron; Vlad Krasnov

doi:10.1109/ARITH.2018.8464690

The Comeback of Reed Solomon Codes

Nir Drucker, Shay Gueron, Vlad Krasnov

Department of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

Distributed storage systems utilize erasure codes to reduce their storage costs while efficiently handling failures. Many of these codes (e. g., Reed-Solomon (RS) codes) rely on Galois Field (GF) arithmetic, which is considered to be fast when the field characteristic is 2. Nevertheless, some developments in the field of erasure codes offer new efficient techniques that require mostly XOR operations, and are thus faster than GF operations. Recently, Intel announced [1] that its future architecture (codename 'Ice Lake') will introduce new set of instructions called Galois Field New Instruction (GF-NI). These instructions allow software flows to perform vector and matrix multiplications over GF (2⁸) on the wide registers that are available on the AVX512 architectures. In this paper, we explain the functionality of these instructions, and demonstrate their usage for some fast computations in GF(2⁸). We also use the Intel^® Intelligent Storage Acceleration Library (ISA-L) in order to estimate potential future improvement for erasure codes that are based on RS codes. Our results predict approx 1.4x speedup for vectorized multiplication, and 1.83x speedup for the actual encoding.

Original language	English
Title of host publication	Proceedings of the 25th International Symposium on Computer Arithmetic, ARITH 2018
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	125-129
Number of pages	5
ISBN (Print)	9781538626122
DOIs	https://doi.org/10.1109/ARITH.2018.8464690
State	Published - 13 Sep 2018
Event	25th International Symposium on Computer Arithmetic, ARITH 2018 - Amherst, United States Duration: 25 Jun 2018 → 27 Jun 2018

Publication series

Name	Proceedings - Symposium on Computer Arithmetic
Volume	2018-June

Conference

Conference	25th International Symposium on Computer Arithmetic, ARITH 2018
Country/Territory	United States
City	Amherst
Period	25/06/18 → 27/06/18

Bibliographical note

Funding Information:
Israel Science Foundation (grant No. 1018/16)

Funding Information:
This research was supported by: The Israel Science Foundation (grant No. 1018/16); The Ministry of Science and Technology, Israel, and the Department of Science and Technology, Government of India; The BIU Center for Research in Applied Cryptography and Cyber Security, in conjunction with the Israel National Cyber Bureau in the Prime Minister’s Office; The Center for Cyber Law and Policy at the University of Haifa.

Publisher Copyright:
© 2018 IEEE.

ASJC Scopus subject areas

Theoretical Computer Science
Software
Hardware and Architecture

Access to Document

10.1109/ARITH.2018.8464690

Cite this

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title = "The Comeback of Reed Solomon Codes",

abstract = "Distributed storage systems utilize erasure codes to reduce their storage costs while efficiently handling failures. Many of these codes (e. g., Reed-Solomon (RS) codes) rely on Galois Field (GF) arithmetic, which is considered to be fast when the field characteristic is 2. Nevertheless, some developments in the field of erasure codes offer new efficient techniques that require mostly XOR operations, and are thus faster than GF operations. Recently, Intel announced [1] that its future architecture (codename 'Ice Lake') will introduce new set of instructions called Galois Field New Instruction (GF-NI). These instructions allow software flows to perform vector and matrix multiplications over GF (28) on the wide registers that are available on the AVX512 architectures. In this paper, we explain the functionality of these instructions, and demonstrate their usage for some fast computations in GF(28). We also use the Intel{\textregistered} Intelligent Storage Acceleration Library (ISA-L) in order to estimate potential future improvement for erasure codes that are based on RS codes. Our results predict approx 1.4x speedup for vectorized multiplication, and 1.83x speedup for the actual encoding.",

author = "Nir Drucker and Shay Gueron and Vlad Krasnov",

note = "Funding Information: Israel Science Foundation (grant No. 1018/16) Funding Information: This research was supported by: The Israel Science Foundation (grant No. 1018/16); The Ministry of Science and Technology, Israel, and the Department of Science and Technology, Government of India; The BIU Center for Research in Applied Cryptography and Cyber Security, in conjunction with the Israel National Cyber Bureau in the Prime Minister{\textquoteright}s Office; The Center for Cyber Law and Policy at the University of Haifa. Publisher Copyright: {\textcopyright} 2018 IEEE.; 25th International Symposium on Computer Arithmetic, ARITH 2018 ; Conference date: 25-06-2018 Through 27-06-2018",

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doi = "10.1109/ARITH.2018.8464690",

language = "English",

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Drucker, N, Gueron, S & Krasnov, V 2018, The Comeback of Reed Solomon Codes. in Proceedings of the 25th International Symposium on Computer Arithmetic, ARITH 2018., 8464690, Proceedings - Symposium on Computer Arithmetic, vol. 2018-June, Institute of Electrical and Electronics Engineers Inc., pp. 125-129, 25th International Symposium on Computer Arithmetic, ARITH 2018, Amherst, United States, 25/06/18. https://doi.org/10.1109/ARITH.2018.8464690

The Comeback of Reed Solomon Codes. / Drucker, Nir; Gueron, Shay; Krasnov, Vlad.
Proceedings of the 25th International Symposium on Computer Arithmetic, ARITH 2018. Institute of Electrical and Electronics Engineers Inc., 2018. p. 125-129 8464690 (Proceedings - Symposium on Computer Arithmetic; Vol. 2018-June).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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N1 - Funding Information: Israel Science Foundation (grant No. 1018/16) Funding Information: This research was supported by: The Israel Science Foundation (grant No. 1018/16); The Ministry of Science and Technology, Israel, and the Department of Science and Technology, Government of India; The BIU Center for Research in Applied Cryptography and Cyber Security, in conjunction with the Israel National Cyber Bureau in the Prime Minister’s Office; The Center for Cyber Law and Policy at the University of Haifa. Publisher Copyright: © 2018 IEEE.

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N2 - Distributed storage systems utilize erasure codes to reduce their storage costs while efficiently handling failures. Many of these codes (e. g., Reed-Solomon (RS) codes) rely on Galois Field (GF) arithmetic, which is considered to be fast when the field characteristic is 2. Nevertheless, some developments in the field of erasure codes offer new efficient techniques that require mostly XOR operations, and are thus faster than GF operations. Recently, Intel announced [1] that its future architecture (codename 'Ice Lake') will introduce new set of instructions called Galois Field New Instruction (GF-NI). These instructions allow software flows to perform vector and matrix multiplications over GF (28) on the wide registers that are available on the AVX512 architectures. In this paper, we explain the functionality of these instructions, and demonstrate their usage for some fast computations in GF(28). We also use the Intel® Intelligent Storage Acceleration Library (ISA-L) in order to estimate potential future improvement for erasure codes that are based on RS codes. Our results predict approx 1.4x speedup for vectorized multiplication, and 1.83x speedup for the actual encoding.

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The Comeback of Reed Solomon Codes

Abstract

Publication series

Conference

Bibliographical note

ASJC Scopus subject areas

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