Novel Polynomial Basis with Fast Fourier Transform and Its Application to Reed-Solomon Erasure Codes
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10.1109-TIT.2016.2608892.pdf
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ArticleKAUST Department
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) DivisionElectrical Engineering Program
Date
2016-09-13Online Publication Date
2016-09-13Print Publication Date
2016-11Permanent link to this record
http://hdl.handle.net/10754/621096
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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.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.Additional Links
http://ieeexplore.ieee.org/document/7565465/ae974a485f413a2113503eed53cd6c53
10.1109/TIT.2016.2608892