Novel Polynomial Basis with Fast Fourier Transform and Its Application to Reed-Solomon Erasure Codes

Handle URI:
http://hdl.handle.net/10754/621096
Title:
Novel Polynomial Basis with Fast Fourier Transform and Its Application to Reed-Solomon Erasure Codes
Authors:
Lin, Sian-Jheng; Al-Naffouri, Tareq Y. ( 0000-0003-2843-5084 ) ; Han, Yunghsiang S.; Chung, Wei-Ho
Abstract:
In this paper, we present a fast Fourier transform (FFT) algorithm over extension binary fields, where the polynomial is represented in a non-standard basis. The proposed Fourier-like transform requires O(h lg(h)) field operations, where h is the number of evaluation points. Based on the proposed Fourier-like algorithm, we then develop the encoding/ decoding algorithms for (n = 2m; k) Reed-Solomon erasure codes. The proposed encoding/erasure decoding algorithm requires O(n lg(n)), in both additive and multiplicative complexities. As the complexity leading factor is small, the proposed algorithms are advantageous in practical applications. Finally, the approaches to convert the basis between the monomial basis and the new basis are proposed.
KAUST Department:
Electrical Engineering Program
Citation:
Lin S-J, Alnaffouri T, Han Y, Chung W-H (2016) Novel Polynomial Basis with Fast Fourier Transform and Its Application to Reed-Solomon Erasure Codes. IEEE Transactions on Information Theory: 1–1. Available: http://dx.doi.org/10.1109/TIT.2016.2608892.
Publisher:
Institute of Electrical and Electronics Engineers (IEEE)
Journal:
IEEE Transactions on Information Theory
Issue Date:
13-Sep-2016
DOI:
10.1109/TIT.2016.2608892
Type:
Article
ISSN:
0018-9448; 1557-9654
Additional Links:
http://ieeexplore.ieee.org/document/7565465/
Appears in Collections:
Articles; Electrical Engineering Program

Full metadata record

DC FieldValue Language
dc.contributor.authorLin, Sian-Jhengen
dc.contributor.authorAl-Naffouri, Tareq Y.en
dc.contributor.authorHan, Yunghsiang S.en
dc.contributor.authorChung, Wei-Hoen
dc.date.accessioned2016-10-20T11:52:17Z-
dc.date.available2016-10-20T11:52:17Z-
dc.date.issued2016-09-13en
dc.identifier.citationLin S-J, Alnaffouri T, Han Y, Chung W-H (2016) Novel Polynomial Basis with Fast Fourier Transform and Its Application to Reed-Solomon Erasure Codes. IEEE Transactions on Information Theory: 1–1. Available: http://dx.doi.org/10.1109/TIT.2016.2608892.en
dc.identifier.issn0018-9448en
dc.identifier.issn1557-9654en
dc.identifier.doi10.1109/TIT.2016.2608892en
dc.identifier.urihttp://hdl.handle.net/10754/621096-
dc.description.abstractIn this paper, we present a fast Fourier transform (FFT) algorithm over extension binary fields, where the polynomial is represented in a non-standard basis. The proposed Fourier-like transform requires O(h lg(h)) field operations, where h is the number of evaluation points. Based on the proposed Fourier-like algorithm, we then develop the encoding/ decoding algorithms for (n = 2m; k) Reed-Solomon erasure codes. The proposed encoding/erasure decoding algorithm requires O(n lg(n)), in both additive and multiplicative complexities. As the complexity leading factor is small, the proposed algorithms are advantageous in practical applications. Finally, the approaches to convert the basis between the monomial basis and the new basis are proposed.en
dc.publisherInstitute of Electrical and Electronics Engineers (IEEE)en
dc.relation.urlhttp://ieeexplore.ieee.org/document/7565465/en
dc.rights(c) 2016 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.htmlen
dc.subjectAdditivesen
dc.subjectComplexity theoryen
dc.subjectDiscrete Fourier transformsen
dc.subjectReed-Solomon codesen
dc.subjectDecodingen
dc.subjectSTEMen
dc.titleNovel Polynomial Basis with Fast Fourier Transform and Its Application to Reed-Solomon Erasure Codesen
dc.typeArticleen
dc.contributor.departmentElectrical Engineering Programen
dc.identifier.journalIEEE Transactions on Information Theoryen
dc.eprint.versionPost-printen
dc.contributor.institutionSchool of Information Science and Technology at University of Science and Technology of China (USTC), Hefei, Chinaen
dc.contributor.institutionDepartment of Electrical Engineering at National Taiwan University of Science and Technologyen
dc.contributor.institutionNational Taipei Universityen
dc.contributor.institutionResearch Center for Information Technology Innovation, Academia Sinicaen
kaust.authorAl-Naffouri, Tareq Y.en
All Items in KAUST are protected by copyright, with all rights reserved, unless otherwise indicated.