Explicit constructions of optimal-access MDS codes with nearly optimal sub-packetization. Explicit constructions of high-rate MDS array codes with optimal repair bandwidth. of 2012 IEEE International Symposium on Information Theory (ISIT), pages 1182–1186, July 2012. Long MDS codes for optimal repair bandwidth. In 58th IEEE Annual Symposium on Foundations of Computer Science, pages 216–227, 2017. Optimal repair of Reed-Solomon codes: Achieving the cut-set bound. Access versus bandwidth in codes for storage. IEEE Transactions on Information Theory, 59(3):1597–1616, March 2013. Exponential distribution is the probability distribution of the time between events in a Poisson point process. Zigzag codes: MDS array codes with optimal rebuilding. A family of optimal locally recoverable codes.
#Exponential vector code code
An explicit, coupled-layer construction of a high-rate MSR code with low sub-packetization level, small field size and all-node repair. of 2015 IEEE International Symposium on Information Theory (ISIT), pages 2051–2055, June 2015. A high-rate MSR code with polynomial sub-packetization level. MDS code constructions with small sub-packetization and near-optimal repair bandwidth. Optimal exact-regenerating codes for distributed storage at the MSR and MBR points via a product-matrix construction. The setup code gives the following variables: Description a vector of coordinates Name Type numpy array numpy array numpy array. Repair optimal erasure codes through hadamard designs. sexpmv. Improved upper bounds on systematiclength for linear minimum storage regenerating codes. MATLAB code for matrix exponential: Scaled and squared subdiagonal Pade approximation. of the 48th Annual ACM SIGACT Symposium on Theory of Computing, STOC 2016, pages 216–226, New York, NY, USA, 2016. An improved sub-packetization bound for minimum storage regenerating codes. of 2016 IEEE International Symposium on Information Theory (ISIT), pages 76–80, July 2016. Minimum storage regenerating codes for all parameters. A survey on network codes for distributed storage. Network coding for distributed storage systems. Asymptotic interference alignment for optimal repair of MDS codes in distributed storage. of Forty Fifth Asilomar Conference on Signals, Systems and Computers (ASILOMAR), pages 1850–1854, Nov 2011. Polynomial length MDS codes with optimal repair in distributed storage.
In Proceedings of the 21st Annual International Symposium on Computer Architecture, pages 245–254, 1994. EVENODD: an optimal scheme for tolerating double disk failures in RAID architectures. In Proceedings of the IEEE International Symposium on Information Theory, pages 2381–2385, 2018. A tight lower bound on the sub-packetization level of optimal-access MSR and MDS codes.
Further our proof is really short, hinging on one key definition that is somewhat inspired by Galois theory. Our work settles a central open question concerning MSR codes that has received much attention. Previously, a lower bound of ≈ exp(√ k/ r), and a tight lower bound for a restricted class of ”optimal access” MSR codes, were known. Our main result is an almost tight lower bound showing that for an MSR code, one must have ℓ ≥ exp(Ω( k/ r)). However, they all suffer from exponentially large Sub-Packetization ℓ ≳ r k/ r. MSR codes are attractive for use in distributed storage systems, and by now a variety of ingenious constructions of MSR codes are available. This implements an optimization where the exponent is represented in base 2, and repeated squaring is used to create a list of relevant powers of the base. Such a code is called minimum storage regenerating (MSR), if any single symbol of a codeword can be recovered by downloading ℓ/ r field elements (which is known to be the least possible) from each of the other symbols. The length ℓ of each codeword symbol is called the Sub-Packetization of the code. An $(n,k,\ell)$-vector MDS code is a $\mathbb)$, and a tight lower bound for a restricted class of "optimal access" MSR codes, were known.An ( n, k,ℓ)-vector MDS code is a F-linear subspace of (F ℓ) n (for some field F) of dimension kℓ, such that any k (vector) symbols of the codeword suffice to determine the remaining r= n− k (vector) symbols.
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