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P V Kumar - One of the best experts on this subject based on the ideXlab platform.
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ISCCSP - Optimality of the Product-Matrix construction for secure MSR regenerating codes
2014 6th International Symposium on Communications Control and Signal Processing (ISCCSP), 2014Co-Authors: B. Sasidharan, K V Rashmi, Nihar B Shah, P V Kumar, K. RamachandranAbstract:In this paper, we consider the security of exact-repair regenerating codes operating at the minimum-storage-regenerating (MSR) point. The security requirement (introduced in Shah et. al.) is that no information about the stored data file must be leaked in the presence of an eavesdropper who has access to the contents of l 1 nodes as well as all the repair traffic entering a second disjoint set of l 2 nodes. We derive an upper bound on the size of a data file that can be securely stored that holds whenever l 2 ≤ d - k + 1. This upper bound proves the optimality of the Product-Matrix-based construction of secure MSR regenerating codes by Shah et. al.
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optimal exact regenerating codes for distributed storage at the msr and mbr points via a Product Matrix construction
IEEE Transactions on Information Theory, 2011Co-Authors: K V Rashmi, Nihar B Shah, P V KumarAbstract:Regenerating codes are a class of distributed storage codes that allow for efficient repair of failed nodes, as compared to traditional erasure codes. An [n, k, d] regenerating code permits the data to be recovered by connecting to any k of the n nodes in the network, while requiring that a failed node be repaired by connecting to any d nodes. The amount of data downloaded for repair is typically much smaller than the size of the source data. Previous constructions of exact-regenerating codes have been confined to the case n=d+1 . In this paper, we present optimal, explicit constructions of (a) Minimum Bandwidth Regenerating (MBR) codes for all values of [n, k, d] and (b) Minimum Storage Regenerating (MSR) codes for all [n, k, d ≥ 2k-2], using a new Product-Matrix framework. The Product-Matrix framework is also shown to significantly simplify system operation. To the best of our knowledge, these are the first constructions of exact-regenerating codes that allow the number n of nodes in the network, to be chosen independent of the other parameters. The paper also contains a simpler description, in the Product-Matrix framework, of a previously constructed MSR code with [n=d+1, k, d ≥ 2k-1].
Yi-sheng Chen - One of the best experts on this subject based on the ideXlab platform.
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Blind channel estimation for single carrier block transmission systems with frequency domain equalization
2008 14th Asia-Pacific Conference on Communications, 2008Co-Authors: Yi-sheng ChenAbstract:We propose a blind channel estimation method for single carrier block transmission systems with frequency domain equalization. The method uses periodic precoding on the source signal before transmission. The estimation of the channel impulse response vector consists of two steps: (1) obtain the channel Product Matrix by solving a group of decoupled linear equations, and (2) obtain the channel impulse response vector by computing the maximal eigenvalue and the associated eigenvector of a Hermitian Matrix formed from the channel Product Matrix. The identifiability condition is very simple. The design of the precoding sequence which minimizes the noise effect and numerical error in covariance Matrix estimation is proposed. Simulations are used to demonstrate the performance of the method.
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Blind-Channel Identification for MIMO Single-Carrier Zero-Padding Block-Transmission Systems
IEEE Transactions on Circuits and Systems I: Regular Papers, 2008Co-Authors: Yi-sheng Chen, Ching-an LinAbstract:We propose a blind identification method for multiple-input multiple-output (MIMO) single-carrier zero-padding block-transmission systems. The method uses periodic precoding on the source signal before transmission. The estimation of the channel impulse response Matrix consists of two steps: 1) obtain the channel Product Matrix by solving a lower-triangular linear system; 2) obtain the channel impulse response Matrix by computing the positive eigenvalues and eigenvectors of a Hermitian Matrix formed from the channel Product Matrix. The method is applicable to MIMO channels with more transmitters or more receivers. A sufficient condition for identifiability is simply that the channel impulse response Matrix is full column rank. The design of the precoding sequence which minimizes the noise effect in covariance Matrix estimation is proposed and the effect of the optimal precoding sequence on channel equalization is discussed. Simulations are used to demonstrate the performance of the method.
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Blind Channel Identification for MIMO Single Carrier Zero Padding Block Transmission Systems
2006 IEEE 7th Workshop on Signal Processing Advances in Wireless Communications, 2006Co-Authors: Yi-sheng Chen, Ching-an LinAbstract:We propose a blind identification method for MIMO single carrier zero padding block transmission systems. The method uses periodic precoding on the source signal before transmission. The estimation of channel impulse response Matrix consists of two steps: (i) obtain the channel Product Matrix by solving a lower-triangular linear system and (ii) obtain the channel impulse response Matrix by computing the positive eigenvalues and eigenvectors of a Hermitian Matrix formed from the channel Product Matrix. A sufficient condition for identifiability is simply that the channel impulse response Matrix is full column rank. The design of the precoding sequence to minimize the noise effect in covariance Matrix estimation is proposed. Simulation examples are used to demonstrate the performance of the method.
K V Rashmi - One of the best experts on this subject based on the ideXlab platform.
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ISCCSP - Optimality of the Product-Matrix construction for secure MSR regenerating codes
2014 6th International Symposium on Communications Control and Signal Processing (ISCCSP), 2014Co-Authors: B. Sasidharan, K V Rashmi, Nihar B Shah, P V Kumar, K. RamachandranAbstract:In this paper, we consider the security of exact-repair regenerating codes operating at the minimum-storage-regenerating (MSR) point. The security requirement (introduced in Shah et. al.) is that no information about the stored data file must be leaked in the presence of an eavesdropper who has access to the contents of l 1 nodes as well as all the repair traffic entering a second disjoint set of l 2 nodes. We derive an upper bound on the size of a data file that can be securely stored that holds whenever l 2 ≤ d - k + 1. This upper bound proves the optimality of the Product-Matrix-based construction of secure MSR regenerating codes by Shah et. al.
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optimal exact regenerating codes for distributed storage at the msr and mbr points via a Product Matrix construction
IEEE Transactions on Information Theory, 2011Co-Authors: K V Rashmi, Nihar B Shah, P V KumarAbstract:Regenerating codes are a class of distributed storage codes that allow for efficient repair of failed nodes, as compared to traditional erasure codes. An [n, k, d] regenerating code permits the data to be recovered by connecting to any k of the n nodes in the network, while requiring that a failed node be repaired by connecting to any d nodes. The amount of data downloaded for repair is typically much smaller than the size of the source data. Previous constructions of exact-regenerating codes have been confined to the case n=d+1 . In this paper, we present optimal, explicit constructions of (a) Minimum Bandwidth Regenerating (MBR) codes for all values of [n, k, d] and (b) Minimum Storage Regenerating (MSR) codes for all [n, k, d ≥ 2k-2], using a new Product-Matrix framework. The Product-Matrix framework is also shown to significantly simplify system operation. To the best of our knowledge, these are the first constructions of exact-regenerating codes that allow the number n of nodes in the network, to be chosen independent of the other parameters. The paper also contains a simpler description, in the Product-Matrix framework, of a previously constructed MSR code with [n=d+1, k, d ≥ 2k-1].
Zhifang Zhang - One of the best experts on this subject based on the ideXlab platform.
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Scalar MSCR Codes via the Product Matrix Construction
IEEE Transactions on Information Theory, 2020Co-Authors: Yaqian Zhang, Zhifang ZhangAbstract:An $(n,k,d)$ cooperative regenerating code provides the optimal-bandwidth repair for any $t~(t\!>\!1)$ node failures in a cooperative way. In particular, an MSCR (minimum storage cooperative regenerating) code retains the same storage overhead as an $(n,k)$ MDS code. Suppose each node stores $\alpha $ symbols which indicates the sub-packetization level of the code. A scalar MSCR code attains the minimum sub-packetization, i.e., $\alpha =d-k+t$ . By now, all existing constructions of scalar MSCR codes restrict to very special parameters, eg. $d=k$ or $k=2$ , etc. In a recent work, Ye and Barg construct MSCR codes for all $n,k,d,t$ , however, their construction needs $\alpha \approx \text {exp}(n^{t})$ which is almost infeasible in practice. In this paper, we give an explicit construction of scalar MSCR codes for all $d\geq \max \{2k-1-t,k\}$ , which covers all possible parameters except the case of $k\leq d\leq 2k-2-t$ when $k . Moreover, as a complementary result, for $k we prove the nonexistence of linear scalar MSCR codes that have invariant repair spaces. Our construction and most of the previous scalar MSCR codes all have invariant repair spaces and this property is appealing in practice because of convenient repair. In this sense, this work presents an almost full description of usual scalar MSCR codes.
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Scalar MSCR Codes via the Product Matrix Construction
arXiv: Information Theory, 2018Co-Authors: Yaqian Zhang, Zhifang ZhangAbstract:An $(n,k,d)$ cooperative regenerating code provides the optimal-bandwidth repair for any $t~(t\!>\!1)$ node failures in a cooperative way. In particular, an MSCR (minimum storage cooperative regenerating) code retains the same storage overhead as an $(n,k)$ MDS code. Suppose each node stores $\alpha$ symbols which indicates the sub-packetization level of the code. A scalar MSCR code attains the minimum sub-packetization, i.e., $\alpha=d-k+t$. By now, all existing constructions of scalar MSCR codes restrict to very special parameters, eg. $d=k$ or $k=2$, etc. In a recent work, Ye and Barg construct MSCR codes for all $n,k,d,t$, however, their construction needs $\alpha\approx{\rm exp}(n^t)$ which is almost infeasible in practice. In this paper, we give an explicit construction of scalar MSCR codes for all $d\geq \max\{2k-1-t,k\}$, which covers all possible parameters except the case of $k\leq d\leq 2k-2-t$ when $k
Tareq Y Alnaffouri - One of the best experts on this subject based on the ideXlab platform.
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a unified form of exact msr codes via Product Matrix frameworks
IEEE Transactions on Information Theory, 2015Co-Authors: Weiho Chung, Tareq Y AlnaffouriAbstract:Regenerating codes represent a class of block codes applicable for distributed storage systems. The $[n,k,d]$ regenerating code has data recovery capability while possessing arbitrary $k$ out of $n$ code fragments, and supports the capability for code fragment regeneration through the use of other arbitrary $d$ fragments, for $k\leq d\leq n-1$ . Minimum storage regenerating (MSR) codes are a subset of regenerating codes containing the minimal size of each code fragment. The first explicit construction of MSR codes that can perform exact regeneration (named exact-MSR codes) for $d\geq 2k-2$ has been presented via a Product-Matrix framework. This paper addresses some of the practical issues on the construction of exact-MSR codes. The major contributions of this paper include as follows. A new Product-Matrix framework is proposed to directly include all feasible exact-MSR codes for $d\geq 2k-2$ . The mechanism for a systematic version of exact-MSR code is proposed to minimize the computational complexities for the process of message-symbol remapping. Two practical forms of encoding matrices are presented to reduce the size of the finite field.
