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Recovery and repair schemes are proposed for shift-exclusive-or (shift-XOR) product-matrix (PM) regenerating codes, which outperform those of the existing PM codes in terms of both communication and computation costs. In particular, for the minimum bandwidth regenerating (MBR) codes, our recovery and repair schemes have the optimal transmission bandwidth, zero decoding auxiliary data space and lower time complexity; for the minimum storage regenerating (MSR) codes, our recovery and repair schemes have smaller transmission bandwidth, smaller decoding auxiliary data space and lower time complexity. Moreover, our schemes involve only XOR operations in recovery and repair and are practical for system implementation. Technically, a procedure is first proposed for solving a system of shift-XOR equations, which plays a similar fundamental role as Gaussian elimination for solving systems of linear equations, and is of independent interest. The recovery and repair of shift-XOR MBR/MSR codes are then decomposed into a sequence of systems of shift-XOR equations, and hence can be solved by a sequence of calls to the procedure for solving a system of shift-XOR equations. As the decomposition of the recovery and repair depends only on the PM construction, but not the specific shift and XOR operations, our recovery and repair schemes can be extended to other MBR/MSR codes using the PM construction.
Ximing Fu; Shenghao Yang; Zhiqing Xiao. Recovery and Repair Schemes for Shift-XOR Regenerating Codes. 2019, 1 .
AMA StyleXiming Fu, Shenghao Yang, Zhiqing Xiao. Recovery and Repair Schemes for Shift-XOR Regenerating Codes. . 2019; ():1.
Chicago/Turabian StyleXiming Fu; Shenghao Yang; Zhiqing Xiao. 2019. "Recovery and Repair Schemes for Shift-XOR Regenerating Codes." , no. : 1.
Identity authentication is the process of verifying users’ validity. Unlike classical key-based authentications, which are built on noiseless channels, this paper introduces a general analysis and design framework for identity authentication over noisy channels. Specifically, the authentication scenarios of single time and multiple times are investigated. For each scenario, the lower bound on the opponent’s success probability is derived, and it is smaller than the classical identity authentication’s. In addition, it can remain the same, even if the secret key is reused. Remarkably, the Cartesian authentication code proves to be helpful for hiding the secret key to maximize the secrecy performance. Finally, we show a potential application of this authentication technique.
Fanfan Zheng; Zhiqing Xiao; Shidong Zhou; Jing Wang; Lianfen Huang. Identity Authentication over Noisy Channels. Entropy 2015, 17, 4940 -4958.
AMA StyleFanfan Zheng, Zhiqing Xiao, Shidong Zhou, Jing Wang, Lianfen Huang. Identity Authentication over Noisy Channels. Entropy. 2015; 17 (12):4940-4958.
Chicago/Turabian StyleFanfan Zheng; Zhiqing Xiao; Shidong Zhou; Jing Wang; Lianfen Huang. 2015. "Identity Authentication over Noisy Channels." Entropy 17, no. 12: 4940-4958.
This paper studies the allocation of information flows in noiseless, memoryless communication networks in the presence of omniscient Byzantine adversary. In such networks, adversary may maliciously modify some edge-flows, and legitimate users should resort to network error correction strategies to transmit data reliably. Unlike prior papers, which focused on the capacities of the networks, we consider the expense of resources used by the flow. Hereby, this paper uses an optimization problem to define the concept of minimum cost network error correction flows. We provide a necessary and sufficient condition of feasibility of the allocation problem, and derive a cut-set outer bound on the feasible region. Using this cut-set bound, we can find the minimum cost network error correction flow in some instances. Moreover, we also consider the relationship between incoming edge-flows and outgoing edge-flows of a vertex. As for the directed acyclic graphs, we propose an algorithm to allocate the network error correction flow. This algorithm is with polynomial time complexity, and proves to be optimal when recoding at intermediate nodes is forbidden. Additionally, in order to justify the necessity of recoding at intermediate nodes, we analyze the benefit of intermediate recoding. On the one hand, we construct a series of instances to prove that intermediate recoding can bring enormous benefits in some networks. On the other hand, numerical analysis shows that the benefit is modest in small random graphs.
Zhiqing Xiao; Yunzhou Li; Ming Zhao; Xibin Xu; Jing Wang. Allocation of Network Error Correction Flow to Combat Byzantine Attacks. IEEE Transactions on Communications 2015, 63, 2605 -2618.
AMA StyleZhiqing Xiao, Yunzhou Li, Ming Zhao, Xibin Xu, Jing Wang. Allocation of Network Error Correction Flow to Combat Byzantine Attacks. IEEE Transactions on Communications. 2015; 63 (7):2605-2618.
Chicago/Turabian StyleZhiqing Xiao; Yunzhou Li; Ming Zhao; Xibin Xu; Jing Wang. 2015. "Allocation of Network Error Correction Flow to Combat Byzantine Attacks." IEEE Transactions on Communications 63, no. 7: 2605-2618.
In distributed multilevel diversity coding, $K$ correlated sources (each with $K$ components) are encoded in a distributed manner such that, given the outputs from any $\alpha$ encoders, the decoder can reconstruct the first $\alpha$ components of each of the corresponding $\alpha$ sources. For this problem, the optimality of a multilayer Slepian-Wolf coding scheme based on binning and superposition is established when $K\leq 3$. The same conclusion is shown to hold for general $K$ under a certain symmetry condition, which generalizes a celebrated result by Yeung and Zhang.
Zhiqing Xiao; Jun Chen; Yunzhou Li; Jing Wang. Distributed Multilevel Diversity Coding. 2015, 1 .
AMA StyleZhiqing Xiao, Jun Chen, Yunzhou Li, Jing Wang. Distributed Multilevel Diversity Coding. . 2015; ():1.
Chicago/Turabian StyleZhiqing Xiao; Jun Chen; Yunzhou Li; Jing Wang. 2015. "Distributed Multilevel Diversity Coding." , no. : 1.
This letter considers the network error-correction capacity in the presence of Byzantine attacks. Unlike prior papers, which assume no delay in any part of networks, we consider the effects of processing delays in the nodes. We prove that these processing delays have no impact on the network error-correction capacity region for any directed network.
Zhiqing Xiao; Yunzhou Li; Xin Su; Jing Wang. Processing Delays Do Not Degrade Network Error-Correction Capacity in Directed Networks. IEEE Communications Letters 2015, 19, 2054 -2057.
AMA StyleZhiqing Xiao, Yunzhou Li, Xin Su, Jing Wang. Processing Delays Do Not Degrade Network Error-Correction Capacity in Directed Networks. IEEE Communications Letters. 2015; 19 (12):2054-2057.
Chicago/Turabian StyleZhiqing Xiao; Yunzhou Li; Xin Su; Jing Wang. 2015. "Processing Delays Do Not Degrade Network Error-Correction Capacity in Directed Networks." IEEE Communications Letters 19, no. 12: 2054-2057.
The essence of authentication is the transmission of unique and irreproducible information. In this paper, the authentication becomes a problem of the secure transmission of the secret key over noisy channels. A general analysis and design framework for message authentication is presented based on the results of Wyner’s wiretap channel. Impersonation and substitution attacks are primarily investigated. Information-theoretic lower and upper bounds on the opponent’s success probability are derived, and the lower bound and the upper bound are shown to match. In general, the fundamental limits on message authentication over noisy channels are fully characterized. Analysis results demonstrate that introducing noisy channels is a reliable way to enhance the security of authentication.
Fanfan Zheng; Zhiqing Xiao; Shidong Zhou; Jing Wang; Lianfen Huang. Message Authentication over Noisy Channels. Entropy 2015, 17, 368 -383.
AMA StyleFanfan Zheng, Zhiqing Xiao, Shidong Zhou, Jing Wang, Lianfen Huang. Message Authentication over Noisy Channels. Entropy. 2015; 17 (1):368-383.
Chicago/Turabian StyleFanfan Zheng; Zhiqing Xiao; Shidong Zhou; Jing Wang; Lianfen Huang. 2015. "Message Authentication over Noisy Channels." Entropy 17, no. 1: 368-383.