The Experts below are selected from a list of 134688 Experts worldwide ranked by ideXlab platform
Walter O. Krawec - One of the best experts on this subject based on the ideXlab platform.
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key Rate Bound of a semi quantum protocol using an entropic uncertainty relation
International Symposium on Information Theory, 2018Co-Authors: Walter O. KrawecAbstract:In this paper we present a new proof technique for semi-quantum key distribution (SQKD) protocols which makes use of a quantum entropic uncertainty relation to Bound an adversary's information. We develop several new techniques for analyzing SQKD protocols; furthermore, our new proof may hold application in the security analysis of other semi-quantum protocols or protocols relying on two-way quantum communication.
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ISIT - Key-Rate Bound of a Semi-Quantum Protocol Using an Entropic Uncertainty Relation
2018 IEEE International Symposium on Information Theory (ISIT), 2018Co-Authors: Walter O. KrawecAbstract:In this paper we present a new proof technique for semi-quantum key distribution (SQKD) protocols which makes use of a quantum entropic uncertainty relation to Bound an adversary's information. We develop several new techniques for analyzing SQKD protocols; furthermore, our new proof may hold application in the security analysis of other semi-quantum protocols or protocols relying on two-way quantum communication.
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Key-Rate Bound of a Semi-Quantum Protocol Using an Entropic Uncertainty Relation
arXiv: Quantum Physics, 2018Co-Authors: Walter O. KrawecAbstract:In this paper we present a new proof technique for semi-quantum key distribution protocols which makes use of a quantum entropic uncertainty relation to Bound an adversary's information. Our new technique provides a more optimistic key-Rate Bound than previous work relying only on noise statistics (as opposed to using additional mismatched measurements which increase the noise tolerance of this protocol, but at the cost of requiring four times the amount of measurement data). Our new technique may hold application in the proof of security of other semi-quantum protocols or protocols relying on two-way quantum communication.
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ISIT - Asymptotic analysis of a three state quantum cryptographic protocol
2016 IEEE International Symposium on Information Theory (ISIT), 2016Co-Authors: Walter O. KrawecAbstract:In this paper we consider a three-state variant of the BB84 quantum key distribution (QKD) protocol. We derive a new lower-Bound on the key Rate of this protocol in the asymptotic scenario and use mismatched measurement outcomes to improve the channel estimation. Our new key Rate Bound remains positive up to an error Rate of 11%, exactly that achieved by the four-state BB84 protocol.
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Asymptotic Analysis of a Three State Quantum Cryptographic Protocol
arXiv: Quantum Physics, 2016Co-Authors: Walter O. KrawecAbstract:In this paper we consider a three-state variant of the BB84 quantum key distribution (QKD) protocol. We derive a new lower-Bound on the key Rate of this protocol in the asymptotic scenario and use mismatched measurement outcomes to improve the channel estimation. Our new key Rate Bound remains positive up to an error Rate of $11\%$, exactly that achieved by the four-state BB84 protocol.
S B Balaji - One of the best experts on this subject based on the ideXlab platform.
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A Tight Rate Bound and Matching Construction for Locally Recoverable Codes With Sequential Recovery From Any Number of Multiple Erasures
IEEE Transactions on Information Theory, 2020Co-Authors: S B Balaji, Ganesh R Kini, P. Vijay KumarAbstract:This paper considers the natural extension of locally recoverable codes (LRC) to the case of ${t} > 1$ erased symbols. While several approaches have been proposed for the handling of multiple erasures, in the approach considered here, the t erased symbols are recovered in succession, each time contacting at most r other symbols for assistance. Under the local-recovery constraint, this sequential approach is the most general and hence offers the maximum possible code Rate. We characterize the Rate of an LRC with sequential recovery for any ${r} \geq 3$ and any t , by first deriving an upper Bound on the code Rate and then constructing a binary code achieving this optimal Rate. The upper Bound derived here proves an earlier conjecture. Our approach permits us to deduce the structure of the parity-check matrix of a Rate-optimal LRC with sequential recovery. The derived structure of parity-check matrix leads to a graphical description of the code used in code construction. A subclass of binary codes that are both Rate and block-length optimal, are shown to correspond to certain regular graphs known as Moore graphs, that have the smallest number of vertices for a given girth. A connection with Tornado codes is also made.
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a tight Rate Bound and a matching construction for locally recoverable codes with sequential recovery from any number of multiple erasures
International Symposium on Information Theory, 2017Co-Authors: S B Balaji, Ganesh R Kini, Vijay P KumarAbstract:An [n, fc] code C is said to be locally recoverable in the presence of a single erasure, and with locality parameter r, if each of the n code symbols of C can be recovered by accessing at most r other code symbols. An [n, k] code is said to be a locally recoverable code with sequential recovery from t erasures, if for any set of s ≤ t erasures, there is an s-step sequential recovery process, in which at each step, a single erased symbol is recovered by accessing at most r other code symbols. This is equivalent to the requirement that for any set of s ≤ t erasures, the dual code contain a codeword whose support contains the coordinate of precisely one of the s erased symbols. In this paper, a tight upper Bound on the Rate of such a code, for any value of number of erasures t and any value r ≥ 3, of the locality parameter is derived. This Bound proves an earlier conjecture due to Song, Cai and Yuen. While the Bound is valid irrespective of the field over which the code is defined, a matching construction of binary codes that are Rate-optimal is also provided, again for any value of t and any value r ≥ 3.
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ISIT - A tight Rate Bound and a matching construction for locally recoverable codes with sequential recovery from any number of multiple erasures
2017 IEEE International Symposium on Information Theory (ISIT), 2017Co-Authors: S B Balaji, Ganesh R Kini, P. Vijay KumarAbstract:An [n, fc] code C is said to be locally recoverable in the presence of a single erasure, and with locality parameter r, if each of the n code symbols of C can be recovered by accessing at most r other code symbols. An [n, k] code is said to be a locally recoverable code with sequential recovery from t erasures, if for any set of s ≤ t erasures, there is an s-step sequential recovery process, in which at each step, a single erased symbol is recovered by accessing at most r other code symbols. This is equivalent to the requirement that for any set of s ≤ t erasures, the dual code contain a codeword whose support contains the coordinate of precisely one of the s erased symbols. In this paper, a tight upper Bound on the Rate of such a code, for any value of number of erasures t and any value r ≥ 3, of the locality parameter is derived. This Bound proves an earlier conjecture due to Song, Cai and Yuen. While the Bound is valid irrespective of the field over which the code is defined, a matching construction of binary codes that are Rate-optimal is also provided, again for any value of t and any value r ≥ 3.
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a tight Rate Bound and a matching construction for locally recoverable codes with sequential recovery from any number of multiple erasures
arXiv: Information Theory, 2016Co-Authors: S B Balaji, Ganesh R Kini, Vijay P KumarAbstract:By a locally recoverable code (LRC), we will in this paper, mean a linear code in which a given code symbol can be recovered by taking a linear combination of at most $r$ other code symbols with $r << k$. A natural extension is to the local recovery of a set of $t$ erased symbols. There have been several approaches proposed for the handling of multiple erasures. The approach considered here, is one of sequential recovery meaning that the $t$ erased symbols are recovered in succession, each time contacting at most $r$ other symbols for assistance in recovery. Under the constraint that each erased symbol be recoverable by contacting at most $r$ other code symbols, this approach is the most general and hence offers maximum possible code Rate. We characterize the maximum possible Rate of an LRC with sequential recovery for any $r \geq 3$ and $t$. We do this by first deriving an upper Bound on code Rate and then going on to construct a {\em binary} code that achieves this optimal Rate. The upper Bound derived here proves a conjecture made earlier relating to the structure (but not the exact form) of the Rate Bound. Our approach also permits us to deduce the structure of the parity-check matrix of a Rate-optimal LRC with sequential recovery. The parity-check matrix in turn, leads to a graphical description of the code. The construction of a binary code having Rate achieving the upper Bound derived here makes use of this description. Interestingly, it turns out that a subclass of binary codes that are both Rate and block-length optimal, correspond to graphs known as Moore graphs that are regular graphs having the smallest number of vertices for a given girth. A connection with Tornado codes is also made in the paper.
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A Tight Rate Bound and a Matching Construction for Locally Recoverable Codes with Sequential Recovery From Any Number of Multiple Erasures
arXiv: Information Theory, 2016Co-Authors: S B Balaji, Ganesh R Kini, P. Vijay KumarAbstract:By a locally recoverable code (LRC), we will in this paper, mean a linear code in which a given code symbol can be recovered by taking a linear combination of at most $r$ other code symbols with $r
Vijay P Kumar - One of the best experts on this subject based on the ideXlab platform.
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a tight Rate Bound and a matching construction for locally recoverable codes with sequential recovery from any number of multiple erasures
International Symposium on Information Theory, 2017Co-Authors: S B Balaji, Ganesh R Kini, Vijay P KumarAbstract:An [n, fc] code C is said to be locally recoverable in the presence of a single erasure, and with locality parameter r, if each of the n code symbols of C can be recovered by accessing at most r other code symbols. An [n, k] code is said to be a locally recoverable code with sequential recovery from t erasures, if for any set of s ≤ t erasures, there is an s-step sequential recovery process, in which at each step, a single erased symbol is recovered by accessing at most r other code symbols. This is equivalent to the requirement that for any set of s ≤ t erasures, the dual code contain a codeword whose support contains the coordinate of precisely one of the s erased symbols. In this paper, a tight upper Bound on the Rate of such a code, for any value of number of erasures t and any value r ≥ 3, of the locality parameter is derived. This Bound proves an earlier conjecture due to Song, Cai and Yuen. While the Bound is valid irrespective of the field over which the code is defined, a matching construction of binary codes that are Rate-optimal is also provided, again for any value of t and any value r ≥ 3.
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a tight Rate Bound and a matching construction for locally recoverable codes with sequential recovery from any number of multiple erasures
arXiv: Information Theory, 2016Co-Authors: S B Balaji, Ganesh R Kini, Vijay P KumarAbstract:By a locally recoverable code (LRC), we will in this paper, mean a linear code in which a given code symbol can be recovered by taking a linear combination of at most $r$ other code symbols with $r << k$. A natural extension is to the local recovery of a set of $t$ erased symbols. There have been several approaches proposed for the handling of multiple erasures. The approach considered here, is one of sequential recovery meaning that the $t$ erased symbols are recovered in succession, each time contacting at most $r$ other symbols for assistance in recovery. Under the constraint that each erased symbol be recoverable by contacting at most $r$ other code symbols, this approach is the most general and hence offers maximum possible code Rate. We characterize the maximum possible Rate of an LRC with sequential recovery for any $r \geq 3$ and $t$. We do this by first deriving an upper Bound on code Rate and then going on to construct a {\em binary} code that achieves this optimal Rate. The upper Bound derived here proves a conjecture made earlier relating to the structure (but not the exact form) of the Rate Bound. Our approach also permits us to deduce the structure of the parity-check matrix of a Rate-optimal LRC with sequential recovery. The parity-check matrix in turn, leads to a graphical description of the code. The construction of a binary code having Rate achieving the upper Bound derived here makes use of this description. Interestingly, it turns out that a subclass of binary codes that are both Rate and block-length optimal, correspond to graphs known as Moore graphs that are regular graphs having the smallest number of vertices for a given girth. A connection with Tornado codes is also made in the paper.
P. Vijay Kumar - One of the best experts on this subject based on the ideXlab platform.
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A Tight Rate Bound and Matching Construction for Locally Recoverable Codes With Sequential Recovery From Any Number of Multiple Erasures
IEEE Transactions on Information Theory, 2020Co-Authors: S B Balaji, Ganesh R Kini, P. Vijay KumarAbstract:This paper considers the natural extension of locally recoverable codes (LRC) to the case of ${t} > 1$ erased symbols. While several approaches have been proposed for the handling of multiple erasures, in the approach considered here, the t erased symbols are recovered in succession, each time contacting at most r other symbols for assistance. Under the local-recovery constraint, this sequential approach is the most general and hence offers the maximum possible code Rate. We characterize the Rate of an LRC with sequential recovery for any ${r} \geq 3$ and any t , by first deriving an upper Bound on the code Rate and then constructing a binary code achieving this optimal Rate. The upper Bound derived here proves an earlier conjecture. Our approach permits us to deduce the structure of the parity-check matrix of a Rate-optimal LRC with sequential recovery. The derived structure of parity-check matrix leads to a graphical description of the code used in code construction. A subclass of binary codes that are both Rate and block-length optimal, are shown to correspond to certain regular graphs known as Moore graphs, that have the smallest number of vertices for a given girth. A connection with Tornado codes is also made.
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ISIT - A tight Rate Bound and a matching construction for locally recoverable codes with sequential recovery from any number of multiple erasures
2017 IEEE International Symposium on Information Theory (ISIT), 2017Co-Authors: S B Balaji, Ganesh R Kini, P. Vijay KumarAbstract:An [n, fc] code C is said to be locally recoverable in the presence of a single erasure, and with locality parameter r, if each of the n code symbols of C can be recovered by accessing at most r other code symbols. An [n, k] code is said to be a locally recoverable code with sequential recovery from t erasures, if for any set of s ≤ t erasures, there is an s-step sequential recovery process, in which at each step, a single erased symbol is recovered by accessing at most r other code symbols. This is equivalent to the requirement that for any set of s ≤ t erasures, the dual code contain a codeword whose support contains the coordinate of precisely one of the s erased symbols. In this paper, a tight upper Bound on the Rate of such a code, for any value of number of erasures t and any value r ≥ 3, of the locality parameter is derived. This Bound proves an earlier conjecture due to Song, Cai and Yuen. While the Bound is valid irrespective of the field over which the code is defined, a matching construction of binary codes that are Rate-optimal is also provided, again for any value of t and any value r ≥ 3.
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A Bound on Rate of Codes with Locality with Sequential Recovery from Multiple Erasures.
arXiv: Information Theory, 2016Co-Authors: Sindhu Balaji, Ganesh R Kini, P. Vijay KumarAbstract:In this paper, we derive an upper Bound on Rate of a code with locality with sequential recovery from multiple erasures for any $r \geq 3$ and any $t>0$ . We also give a construction of codes achieving our Rate Bound for any $r$ and $t \in 2\mathbb{Z_{+}}$.
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A Tight Rate Bound and a Matching Construction for Locally Recoverable Codes with Sequential Recovery From Any Number of Multiple Erasures
arXiv: Information Theory, 2016Co-Authors: S B Balaji, Ganesh R Kini, P. Vijay KumarAbstract:By a locally recoverable code (LRC), we will in this paper, mean a linear code in which a given code symbol can be recovered by taking a linear combination of at most $r$ other code symbols with $r
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Binary Codes with Locality for Four Erasures.
arXiv: Information Theory, 2016Co-Authors: Sindhu Balaji, K. P. Prasanth, P. Vijay KumarAbstract:In this paper, codes with locality for four erasures are considered. An upper Bound on the Rate of codes with locality with sequential recovery from four erasures is derived. The Rate Bound derived here is field independent. An optimal construction for binary codes meeting this Rate Bound is also provided. The construction is based on regular graphs of girth $6$ and employs the sequential approach of locally recovering from multiple erasures. An extension of this construction that geneRates codes which can sequentially recover from five erasures is also presented.
Ganesh R Kini - One of the best experts on this subject based on the ideXlab platform.
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A Tight Rate Bound and Matching Construction for Locally Recoverable Codes With Sequential Recovery From Any Number of Multiple Erasures
IEEE Transactions on Information Theory, 2020Co-Authors: S B Balaji, Ganesh R Kini, P. Vijay KumarAbstract:This paper considers the natural extension of locally recoverable codes (LRC) to the case of ${t} > 1$ erased symbols. While several approaches have been proposed for the handling of multiple erasures, in the approach considered here, the t erased symbols are recovered in succession, each time contacting at most r other symbols for assistance. Under the local-recovery constraint, this sequential approach is the most general and hence offers the maximum possible code Rate. We characterize the Rate of an LRC with sequential recovery for any ${r} \geq 3$ and any t , by first deriving an upper Bound on the code Rate and then constructing a binary code achieving this optimal Rate. The upper Bound derived here proves an earlier conjecture. Our approach permits us to deduce the structure of the parity-check matrix of a Rate-optimal LRC with sequential recovery. The derived structure of parity-check matrix leads to a graphical description of the code used in code construction. A subclass of binary codes that are both Rate and block-length optimal, are shown to correspond to certain regular graphs known as Moore graphs, that have the smallest number of vertices for a given girth. A connection with Tornado codes is also made.
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a tight Rate Bound and a matching construction for locally recoverable codes with sequential recovery from any number of multiple erasures
International Symposium on Information Theory, 2017Co-Authors: S B Balaji, Ganesh R Kini, Vijay P KumarAbstract:An [n, fc] code C is said to be locally recoverable in the presence of a single erasure, and with locality parameter r, if each of the n code symbols of C can be recovered by accessing at most r other code symbols. An [n, k] code is said to be a locally recoverable code with sequential recovery from t erasures, if for any set of s ≤ t erasures, there is an s-step sequential recovery process, in which at each step, a single erased symbol is recovered by accessing at most r other code symbols. This is equivalent to the requirement that for any set of s ≤ t erasures, the dual code contain a codeword whose support contains the coordinate of precisely one of the s erased symbols. In this paper, a tight upper Bound on the Rate of such a code, for any value of number of erasures t and any value r ≥ 3, of the locality parameter is derived. This Bound proves an earlier conjecture due to Song, Cai and Yuen. While the Bound is valid irrespective of the field over which the code is defined, a matching construction of binary codes that are Rate-optimal is also provided, again for any value of t and any value r ≥ 3.
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ISIT - A tight Rate Bound and a matching construction for locally recoverable codes with sequential recovery from any number of multiple erasures
2017 IEEE International Symposium on Information Theory (ISIT), 2017Co-Authors: S B Balaji, Ganesh R Kini, P. Vijay KumarAbstract:An [n, fc] code C is said to be locally recoverable in the presence of a single erasure, and with locality parameter r, if each of the n code symbols of C can be recovered by accessing at most r other code symbols. An [n, k] code is said to be a locally recoverable code with sequential recovery from t erasures, if for any set of s ≤ t erasures, there is an s-step sequential recovery process, in which at each step, a single erased symbol is recovered by accessing at most r other code symbols. This is equivalent to the requirement that for any set of s ≤ t erasures, the dual code contain a codeword whose support contains the coordinate of precisely one of the s erased symbols. In this paper, a tight upper Bound on the Rate of such a code, for any value of number of erasures t and any value r ≥ 3, of the locality parameter is derived. This Bound proves an earlier conjecture due to Song, Cai and Yuen. While the Bound is valid irrespective of the field over which the code is defined, a matching construction of binary codes that are Rate-optimal is also provided, again for any value of t and any value r ≥ 3.
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a tight Rate Bound and a matching construction for locally recoverable codes with sequential recovery from any number of multiple erasures
arXiv: Information Theory, 2016Co-Authors: S B Balaji, Ganesh R Kini, Vijay P KumarAbstract:By a locally recoverable code (LRC), we will in this paper, mean a linear code in which a given code symbol can be recovered by taking a linear combination of at most $r$ other code symbols with $r << k$. A natural extension is to the local recovery of a set of $t$ erased symbols. There have been several approaches proposed for the handling of multiple erasures. The approach considered here, is one of sequential recovery meaning that the $t$ erased symbols are recovered in succession, each time contacting at most $r$ other symbols for assistance in recovery. Under the constraint that each erased symbol be recoverable by contacting at most $r$ other code symbols, this approach is the most general and hence offers maximum possible code Rate. We characterize the maximum possible Rate of an LRC with sequential recovery for any $r \geq 3$ and $t$. We do this by first deriving an upper Bound on code Rate and then going on to construct a {\em binary} code that achieves this optimal Rate. The upper Bound derived here proves a conjecture made earlier relating to the structure (but not the exact form) of the Rate Bound. Our approach also permits us to deduce the structure of the parity-check matrix of a Rate-optimal LRC with sequential recovery. The parity-check matrix in turn, leads to a graphical description of the code. The construction of a binary code having Rate achieving the upper Bound derived here makes use of this description. Interestingly, it turns out that a subclass of binary codes that are both Rate and block-length optimal, correspond to graphs known as Moore graphs that are regular graphs having the smallest number of vertices for a given girth. A connection with Tornado codes is also made in the paper.
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A Bound on Rate of Codes with Locality with Sequential Recovery from Multiple Erasures.
arXiv: Information Theory, 2016Co-Authors: Sindhu Balaji, Ganesh R Kini, P. Vijay KumarAbstract:In this paper, we derive an upper Bound on Rate of a code with locality with sequential recovery from multiple erasures for any $r \geq 3$ and any $t>0$ . We also give a construction of codes achieving our Rate Bound for any $r$ and $t \in 2\mathbb{Z_{+}}$.
