Systematic MDS Erasure Codes Based on Vandermonde Matrices

Lacan, Jérôme; Fimes, Jérôme

doi:10.1109/lcomm.2004.833807

Cited by 101 publications

(70 citation statements)

References 7 publications

(12 reference statements)

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“…As a result, the following problems are encountered when working with R-S codes for packet level FEC: (i) the code rates (parameters) are limited and (ii) the encoding and decoding processes are computationally intensive. Moreover, it has been shown that the Vandermonde matrix, based on the elements taken from the finite GF, is not always non-singular [9].…”

Section: Linear Block Codesmentioning

confidence: 99%

Vandermonde matrix packet-level FEC for joint recovery from errors and packet loss

Al‐Shaikhi

Ilow

2008

2008 IEEE 19th International Symposium on Personal, Indoor and Mobile Radio Communications

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Abstract-Due to layer interactions, packets in cross layer protocol designs are impaired with both errors and packet loss, where the latter is also referred to as a packet erasure. In realtime applications, packet-level forward error correction (FEC) schemes are favorable candidates to enhance the performance of such protocols without retransmission. This paper proposes to use one type of code to recover from both impairments. In particular, the approach builds on recently introduced packet oriented systematic block codes in which parity matrix depends on the Vandermonde structure with shift operators. These codes are maximum distance separable (MDS) and have the advantage over other MDS codes of simple encoding/decoding processes. At the packet level, de-coupling of erasure recovery and the error correction processes is a challenging task, and this paper explores the advantages of packet-level product of two codes: one for erasure recovery and the other for error correction. Monte Carlo simulations show that the throughput of the proposed system improves when applying both error correction and erasure recovery compared to a system applying erasure-only recovery with equivalent overall minimum distance.

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Section: Linear Block Codesmentioning

confidence: 99%

Vandermonde matrix packet-level FEC for joint recovery from errors and packet loss

Al‐Shaikhi

Ilow

2008

2008 IEEE 19th International Symposium on Personal, Indoor and Mobile Radio Communications

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“…Although in some ciphers the possibility of random selection of MDS matrices with some constraint is provided [23]. In this context we would like to mention that in papers [6,7,12,13,17,23], new constructions of MDS matrices are provided. In [6], authors construct lightweight MDS matrices from companion matrices by exhaustive search.…”

Section: Introductionmentioning

confidence: 99%

“…In [12], authors construct efficient 4×4 and 8×8 matrices to be used in block ciphers. In [13,17], authors constructed involutory MDS matrices using Vandermonde matrices. In [23], authors construct new involutory MDS matrices using properties of Cauchy matrices.…”

Section: Introductionmentioning

confidence: 99%

On Constructions of MDS Matrices from Companion Matrices for Lightweight Cryptography

Gupta

Ray

2013

Security Engineering and Intelligence Informatics

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Abstract. Maximum distance separable (MDS) matrices have applications not only in coding theory but also are of great importance in the design of block ciphers and hash functions. It is highly nontrivial to find MDS matrices which could be used in lightweight cryptography. In a crypto 2011 paper, Guo et. al. We also propose more generic constructions of MDS matrices e.g. we construct lightweight 4 × 4 and 5 × 5 MDS matrices over F2n for all n ≥ 4. An algorithm is presented to check if a given matrix is MDS. The algorithm follows from the basic properties of MDS matrix and is easy to implement.

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“…Soro and Lacan [14] proposed a Reed-Solomon erasure coding algorithm with complexity O(n log n) in both encoding and decoding. Lacan and Fimes [15] investigated a systematic MDS erasure coding algorithm based on Vandermonde matrices. For the case k/n ≥ 1/2, Lin and Chung [38] present a (n, k) IDA with complexities O(n log(n−k)) in encoding and decoding.…”

mentioning

confidence: 99%

“…By our survey on the (n, k) erasure coding algorithms over Fermat field, the best records of encoding algorithm take O(n log n) operations [12], [13], [14] and the decoding algorithms take O(n log n) [14] or O(k log 2 k) [15] operations. In this paper, we propose a fast (n, k) IDA based on erasure Reed-Solomon coding systems over Fermat fields.…”

mentioning

confidence: 99%

An Efficient <formula formulatype="inline"><tex Notation="TeX">$(n,k)$</tex> </formula> Information Dispersal Algorithm Based on Fermat Number Transforms

Lin

Chung

2013

IEEE Trans.Inform.Forensic Secur.

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Abstract-The (n, k) information dispersal algorithm (IDA) is a coding technique converting a digital source file into n small digital files (shadows), and the receipt of any k out of the n shadows can losslessly reconstruct the source file. This paper presents an encoding and two decoding algorithms of (n, k) IDA via the fast Fermat number transform (FNT). The proposed encoding algorithm requires O(n log k) arithmetic operations, and the two decoding algorithms have complexities O(n log k) and O(k log 2 k) for a reasonably large file. As compared with existing work, the proposed algorithms generate significant improvement in the throughput in the low code rate k/n ≤ 1/2 settings.

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Systematic MDS Erasure Codes Based on Vandermonde Matrices

Cited by 101 publications

References 7 publications

Vandermonde matrix packet-level FEC for joint recovery from errors and packet loss

Vandermonde matrix packet-level FEC for joint recovery from errors and packet loss

On Constructions of MDS Matrices from Companion Matrices for Lightweight Cryptography

An Efficient <formula formulatype="inline"><tex Notation="TeX">$(n,k)$</tex> </formula> Information Dispersal Algorithm Based on Fermat Number Transforms

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