Elsevier

Theoretical Computer Science

Volume 520, 6 February 2014, Pages 111-123
Theoretical Computer Science

Improved probabilistic decoding of interleaved Reed–Solomon codes and folded Hermitian codes

https://doi.org/10.1016/j.tcs.2013.10.025Get rights and content
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Abstract

Probabilistic simultaneous polynomial reconstruction algorithm of Bleichenbacher, Kiayias, and Yung is extended to the polynomials whose degrees are allowed to be distinct. Specifically, for a finite field F, positive integers n, r, t and distinct elements z1,z2,,znF, we present a probabilistic algorithm which can recover polynomials p1,p2,,prF[x] of degree less than k1,k2,,kr respectively for a given instance yi,1,,yi,ri=1n satisfying pl(zi)=yi,l for all l{1,2,,r} and for all iI{1,2,,n} such that |I|=t with probability at least 1nt|F| and with time complexity at most O(rn4) if tmax{k1,k2,,kr,n+j=1rkjr+1}. Next, by using this algorithm, we present a probabilistic decoder for interleaved Reed–Solomon codes. It is observed that interleaved Reed–Solomon codes over F with rate R can be decoded up to burst error rate rr+1(1R) probabilistically for an interleaving parameter r. Then, it is proved that q-folded Hermitian codes over Fq2q with rate R can be decoded up to error rate qq+1(1R) probabilistically.

Keywords

Simultaneous polynomial reconstruction
Interleaved Reed–Solomon codes
Reed–Solomon codes
Folded Hermitian codes

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