The Experts below are selected from a list of 57 Experts worldwide ranked by ideXlab platform
Venkatesan Guruswami - One of the best experts on this subject based on the ideXlab platform.
-
an exponential lower bound on the sub packetization of msr codes
Symposium on the Theory of Computing, 2019Co-Authors: Omar Alrabiah, Venkatesan GuruswamiAbstract:An (n,k,l)-vector MDS code is a F-linear subspace of (Fl)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. The length l of each codeword symbol is called the Sub-Packetization of the code. 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. MSR codes are attractive for use in distributed storage systems, and by now a variety of ingenious constructions of MSR codes are available. However, they all suffer from exponentially large Sub-Packetization l ≳ rk/r. Our main result is an almost tight lower bound showing that for an MSR code, one must have l ≥ exp(Ω(k/r)). 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 work settles a central open question concerning MSR codes that has received much attention. Further our proof is really short, hinging on one Key Definition that is somewhat inspired by Galois theory.
-
an exponential lower bound on the sub packetization of msr codes
arXiv: Information Theory, 2019Co-Authors: Omar Alrabiah, Venkatesan GuruswamiAbstract:An $(n,k,\ell)$-vector MDS code is a $\mathbb{F}$-linear subspace of $(\mathbb{F}^\ell)^n$ (for some field $\mathbb{F}$) of dimension $k\ell$, such that any $k$ (vector) symbols of the codeword suffice to determine the remaining $r=n-k$ (vector) symbols. The length $\ell$ of each codeword symbol is called the sub-packetization of the code. Such a code is called minimum storage regenerating (MSR), if any single symbol of a codeword can be recovered by downloading $\ell/r$ field elements (which is known to be the least possible) from each of the other symbols. MSR codes are attractive for use in distributed storage systems, and by now a variety of ingenious constructions of MSR codes are available. However, they all suffer from exponentially large sub-packetization $\ell \gtrsim r^{k/r}$. Our main result is an almost tight lower bound showing that for an MSR code, one must have $\ell \ge \exp(\Omega(k/r))$. Previously, a lower bound of $\approx \exp(\sqrt{k/r})$, and a tight lower bound for a restricted class of "optimal access" MSR codes, were known. Our work settles a central open question concerning MSR codes that has received much attention. Further our proof is really short, hinging on one Key Definition that is somewhat inspired by Galois theory.
Omar Alrabiah - One of the best experts on this subject based on the ideXlab platform.
-
an exponential lower bound on the sub packetization of msr codes
Symposium on the Theory of Computing, 2019Co-Authors: Omar Alrabiah, Venkatesan GuruswamiAbstract:An (n,k,l)-vector MDS code is a F-linear subspace of (Fl)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. The length l of each codeword symbol is called the Sub-Packetization of the code. 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. MSR codes are attractive for use in distributed storage systems, and by now a variety of ingenious constructions of MSR codes are available. However, they all suffer from exponentially large Sub-Packetization l ≳ rk/r. Our main result is an almost tight lower bound showing that for an MSR code, one must have l ≥ exp(Ω(k/r)). 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 work settles a central open question concerning MSR codes that has received much attention. Further our proof is really short, hinging on one Key Definition that is somewhat inspired by Galois theory.
-
an exponential lower bound on the sub packetization of msr codes
arXiv: Information Theory, 2019Co-Authors: Omar Alrabiah, Venkatesan GuruswamiAbstract:An $(n,k,\ell)$-vector MDS code is a $\mathbb{F}$-linear subspace of $(\mathbb{F}^\ell)^n$ (for some field $\mathbb{F}$) of dimension $k\ell$, such that any $k$ (vector) symbols of the codeword suffice to determine the remaining $r=n-k$ (vector) symbols. The length $\ell$ of each codeword symbol is called the sub-packetization of the code. Such a code is called minimum storage regenerating (MSR), if any single symbol of a codeword can be recovered by downloading $\ell/r$ field elements (which is known to be the least possible) from each of the other symbols. MSR codes are attractive for use in distributed storage systems, and by now a variety of ingenious constructions of MSR codes are available. However, they all suffer from exponentially large sub-packetization $\ell \gtrsim r^{k/r}$. Our main result is an almost tight lower bound showing that for an MSR code, one must have $\ell \ge \exp(\Omega(k/r))$. Previously, a lower bound of $\approx \exp(\sqrt{k/r})$, and a tight lower bound for a restricted class of "optimal access" MSR codes, were known. Our work settles a central open question concerning MSR codes that has received much attention. Further our proof is really short, hinging on one Key Definition that is somewhat inspired by Galois theory.
C. Jaco Klok - One of the best experts on this subject based on the ideXlab platform.
-
TRACHEAE & TRACHEOLES: A FORTUITOUS DISCOVERY REFINES A Key Definition
Journal of Experimental Biology, 2011Co-Authors: C. Jaco KlokAbstract:![Figure][1] It is always interesting when a seemingly minor study actually contributes significantly to our understanding of a Key concept in animal biology. A Key concept in the field of insect respiratory biology is understanding the structure, function and formation of the insect tracheal
Shi Pei-sha - One of the best experts on this subject based on the ideXlab platform.
-
Analysis of Unified Identity Manager Service Model in Network
Computers & Security, 2013Co-Authors: Shi Pei-shaAbstract:This paper made an analysis of unified identity manage service combined identify management with service. By introducing the Key Definition of identity manage model and present the unified identity service diagrammatic figure, then synthesize technical framework of Internet of Things and network structure of MobileInternet put forward the unified identity service model separately.
Graeme Mackenzie - One of the best experts on this subject based on the ideXlab platform.
-
Essence of being a doctor: productivity may be Key Definition.
BMJ (Clinical research ed.), 2003Co-Authors: Graeme MackenzieAbstract:EDITOR—With reference to Kmietowicz's news item on defining the essence of being a doctor,1 productivity may well be the answer to defining the difference between a nurse practitioner and a general practitioner, which I …
