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Quantized network coding for correlated sources

EURASIP JOURNAL ON WIRELESS COMMUNICATIONS AND networkING 2014年第1期2014卷 1页

作者： Nabaee, Mahdy Labeau, Fabrice McGill Univ Dept Elect & Comp Engn Montreal PQ Canada

In this paper, we present a data gathering technique for sensor networks that exploits correlation between sensor data at different locations in the network. Contrary to distributed source coding, our method does not rely on knowledge of the source correlation model in each node although this knowledge is required at the decoder node. Similar to network coding, our proposed method (which we call Quantized network coding) propagates mixtures of packets through the network. The main conceptual difference between our technique and other existing methods is that Quantized network coding operates on the field of real numbers and not on a finite field. By exploiting principles borrowed from compressed sensing, we show that the proposed technique can achieve a good approximation of the network data at the sink node with only a few packets received and that this approximation gets progressively better as the number of received packets increases. We explain in the paper the theoretical foundation for the algorithm based on an analysis of the restricted isometry property of the corresponding measurement matrices. Extensive simulations comparing the proposed Quantized network coding to classic network coding and packet forwarding scenarios demonstrate its delay/distortion advantage.

关键词： linear network coding Distributed source coding Compressed sensing Restricted isometry property l(1) minimization

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Multicast network coding and Field Sizes

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IEEE TRANSACTIONS ON INFORMATION THEORY 2015年第11期61卷 6182-6191页

作者： Sun, Qifu Tyler Yin, Xunrui Li, Zongpeng Long, Keping Univ Sci & Technol Beijing Sch Comp & Commun Engn Beijing 100083 Peoples R China Univ Calgary Dept Comp Sci Calgary AB T2N 1N4 Canada Wuhan Univ Dept Comp Wuhan 430072 Peoples R China

In an acyclic multicast network, it is well known that a linear network coding solution over GF(q) exists when q is sufficiently large. In particular, for each prime power q no smaller than the number of receivers, a linear solution over GF(q) can be efficiently constructed. In this paper, we reveal that a linear solution over a given finite field does not necessarily imply the existence of a linear solution over all larger finite fields. In particular, we prove by construction that: 1) for every omega >= 3, there is a multicast network with source outdegree omega linearly solvable over GF(7) but not over GF(8), and another multicast network linearly solvable over GF(16) but not over GF(17);2) there is a multicast network linearly solvable over GF(5) but not over such GF(q) that q > 5 is a Mersenne prime plus 1, which can be extremely large;3) a multicast network linearly solvable over GF(q(m1)) and over GF(q(m2)) is not necessarily linearly solvable over GF(q(m1+m2));and 4) there exists a class of multicast networks with a set T of receivers such that the minimum field size q(min) for a linear solution over GF(q(min)) is lower bounded by Theta(root vertical bar T vertical bar), but not every larger field than GF(q(min)) suffices to yield a linear solution. The insight brought from this paper is that not only the field size but also the order of subgroups in the multiplicative group of a finite field affects the linear solvability of a multicast network.

关键词： linear network coding multicast network field size lower bound Mersenne prime

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Evolutionary Minimization of network coding Resources

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APPLIED ARTIFICIAL INTELLIGENCE 2014年第9期28卷 837-858页

作者： Karunarathne, Lalith P. Leeson, Mark S. Hines, Evor L. Univ Warwick Sch Engn Coventry CV4 7AL W Midlands England

A method to identify feasible minimal network coding configurations between a source and a set of receivers without altering or modifying the established network infrastructure is proposed. The approach minimizes the resources used for multicast coding while achieving the desired throughput in the multicast scenario. Because the problem of identifying minimal configurations of a graph is known to be NP-hard, our method first identifies candidate minimal configurations and then searches for the optimal ones using a genetic algorithm (GA). Because the optimization process considers the number of coding nodes, the mean number of coding node input links and the sharing of resources by sinks, the problem is thus a multiobjective problem. Two multiobjective algorithms, MOGA and VEGA, are chosen to solve the problem because they are simple enough not to place heavy demands on source nodes when the minimal configuration is sought. The optimization process is investigated by the simulation of a range of randomly generated networks of varying sizes. Performance differences between the multiple-objective GAs are observed, which seem to arise from the difference in their methods of searching. Nevertheless, both methods perform well in terms of identifying feasible minimal configurations with optimized coding resources. The performance is assessed by comparing the optimized solutions with randomly chosen starting configurations. There are always reductions in the number of coding nodes used, typically 50%, and resource sharing is multiplied by several times. Typical mean in-link savings are 10% but may range from zero to close to 30%. We thus show that relatively simple multiple-objective GAs can deliver optimized minimal coding configurations for the network coding multicast problem. Moreover, the approach here offers an improvement over solutions in the literature because our method remains feasible for relatively large networks and its implementation at the source simplifies

关键词： Multiple criteria decision making Mathematical optimization Artificial intelligence Evolutionary algorithms linear network coding Genetic algorithms

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Information security in a random network coding network

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PROBLEMS OF INFORMATION TRANSMISSION 2013年第2期49卷 179-191页

作者： Gabidulin, E. M. Pilipchuk, N. I. Honary, B. Rashwan, H. State Univ Moscow Inst Phys & Technol Moscow Russia Univ Lancaster Lancaster LA1 4YW England

We consider a communication network with random network coding which can be attacked by adversaries of two types. One of them can wiretap original packets outgoing from source to destination. The other can insert its own packets into information flow, which are wrong messages for the receiver. To provide secure communication, we use a scheme based on combining the GPT (Gabidulin-Paramonov-Tretjakov) public key cryptosystem and SKK (Silva-Kschischang-Koetter) codes. Encrypted packets are transmitted to the destination through wired channels. Performance of this system is investigated. The main result is that the proposed scheme is secure against wiretapping and insertion attacks under some conditions which depend on rank code parameters.

关键词： linear network coding CRYPTOSYSTEMS DATA encryption (Computer science) WIRETAPPING INFORMATION technology -- Security measures

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A Secure network coding Based on Broadcast Encryption in SDN

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MATHEMATICAL PROBLEMS IN ENGINEERING 2016年第1期2016卷 1-8页

作者： Chen, Yue Jia, Hongyong Huang, Kaixiang Lan, Julong Yan, Xincheng State Key Lab Math Engn & Adv Comp Zhengzhou 450001 Peoples R China China Natl Digital Switching Syst Engn & Technol Zhengzhou 450002 Peoples R China

By allowing intermediate nodes to encode the received packets before sending them out, network coding improves the capacity and robustness of multicast applications. But it is vulnerable to the pollution attacks. Some signature schemes were proposed to thwart such attacks, but most of them need to be homomorphic that the keys cannot be generated and managed easily. In this paper, we propose a novel fast and secure switch network coding multicast (SSNC) on the software defined networks (SDN). In our scheme, the complicated securemulticastmanagement was separated from the fast data transmission based on the SDN. Multiplemulticasts will be aggregated to onemulticast group according to the requirements of services and the network status. Then, the controller will route aggregated multicast group with network coding;only the trusted switch will be allowed to join the network coding by using broadcast encryption. The proposed scheme can use the traditional cryptography without homomorphy, which greatly reduces the complexity of the computation and improves the efficiency of transmission.

关键词： linear network coding ENCRYPTION protocols SOFTWARE-defined networking (Computer network technology) ROBUST statistics MULTICASTING (Computer networks)

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Compute-and-Forward network coding Design over Multi-Source Multi-Relay Channels

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IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS 2012年第9期11卷 3348-3357页

作者： Wei, Lili Chen, Wen Shanghai Jiao Tong Univ Dept Elect Engn Shanghai 200030 Peoples R China Xidian Univ SKL ISN Xian Peoples R China Shanghai Jiao Tong Univ Inst Signal Proc & Syst Shanghai 200030 Peoples R China

network coding is a new and promising paradigm for modern communication networks by allowing intermediate nodes to mix messages received from multiple sources. Compute-and-forward strategy is one category of network coding in which a relay will decode and forward a linear combination of source messages according to the observed channel coefficients, based on the algebraic structure of lattice codes. The destination will recover all transmitted messages if enough linear equations are received. In this work, we design in a system level, the compute-and-forward network coding coefficients by Fincke-Pohst based candidate set searching algorithm and network coding system matrix constructing algorithm, such that by those proposed algorithms, the transmission rate of the multi-source multi-relay system is maximized. Numerical results demonstrate the effectiveness of our proposed algorithms.

关键词： Compute-and-forward network coding linear network coding lattice codes cooperative relay channel

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A new method for ensuring anonymity and security in network coding

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PROBLEMS OF INFORMATION TRANSMISSION 2015年第1期51卷 75-81页

作者： Trushina, O. V. Gabidulin, E. M. State Univ Moscow Inst Phys & Technol Moscow Russia

We propose a method for providing anonymity and security of data transmission in networks with network coding with multiple sources and receivers. An external passive adversary is assumed to be present in the network. It is required to organize message transmission in such a manner that the adversary cannot trace a message route. The proposed method is a modification of a secure transmission scheme based on coset coding. We show that using an additional operation at relaying nodes enables to remove statistical dependence between incoming and outgoing messages of the relaying nodes. This makes tracing message routes impossible. An overlay network between a source and a receiver must be constructed due to restrictions on routes between the source and receiver: the minimum cut between two successive nodes must be not less than the number of packets in the encoded source message.

关键词： ANONYMITY COMPUTER network resources DATA transmission systems COMPUTER networks linear network coding MODULATION coding

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On network coding for Sum-networks

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IEEE TRANSACTIONS ON INFORMATION THEORY 2012年第1期58卷 50-63页

作者： Rai, Brijesh Kumar Dey, Bikash Kumar Indian Inst Technol Dept Elect Engn Bombay Maharashtra India

A directed acyclic network is considered where all the terminals need to recover the sum of the symbols generated at all the sources. We call such a network a sum-network. It is shown that there exists a solvably (and linear solvably) equivalent sum-network for any multiple-unicast network, and thus for any directed acyclic communication network. It is also shown that there exists a linear solvably equivalent multiple-unicast network for every sum-network. It is shown that for any set of polynomials having integer coefficients, there exists a sum-network which is scalar linear solvable over a finite field if and only if the polynomials have a common root in. For any finite or cofinite set of prime numbers, a network is constructed which has a vector linear solution of any length if and only if the characteristic of the alphabet field is in the given set. The insufficiency of linear network coding and unachievability of the network coding capacity are proved for sum-networks by using similar known results for communication networks. Under fractional vector linear network coding, a sum-network and its reverse network are shown to be equivalent. However, under nonlinear coding, it is shown that there exists a solvable sum-network whose reverse network is not solvable.

关键词： Function computation linear network coding network coding polynomial equations solvability

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Universal Secure network coding via Rank-Metric Codes

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IEEE TRANSACTIONS ON INFORMATION THEORY 2011年第2期57卷 1124-1135页

作者： Silva, Danilo Kschischang, Frank R. Univ Toronto Edward S Rogers Sr Dept Elect & Comp Engn Toronto ON M5S 3G4 Canada

The problem of securing a network coding communication system against an eavesdropper is considered. The network implements linear network coding to deliver n packets from source to each receiver, and the adversary can eavesdrop on mu arbitrarily chosen links. The objective is to provide reliable communication to all receivers, while guaranteeing that the source information remains information-theoretically secure from the adversary. A coding scheme is proposed that can achieve the maximum possible rate of n - mu packets. The scheme, which is based on rank-metric codes, has the distinctive property of being universal: it can be applied on top of any communication network without requiring knowledge of or any modifications on the underlying linear network code. The only requirement of the scheme is that the packet length be at least n, which is shown to be strictly necessary for universal communication at the maximum rate. A further scenario is considered where the adversary is allowed not only to eavesdrop but also to inject up to t erroneous packets into the network, and the network may suffer from a rank deficiency of at most rho. In this case, the proposed scheme can be extended to achieve the rate of n - rho - 2t - mu packets. This rate is shown to be optimal under the assumption of zero-error communication.

关键词： Error correction information-theoretic security linear network coding rank-metric codes secrecy capacity wiretap channel

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Minimum-Energy Wireless Real-Time Multicast by Joint network coding and Scheduling Optimization

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MATHEMATICAL PROBLEMS IN ENGINEERING 2015年第1期2015卷 1-9页

作者： Tan, Guoping Zhu, Yandan Li, Yueheng Zhang, Lili Xu, Jing Hohai Univ Coll Comp & Informat Engn Nanjing 210098 Jiangsu Peoples R China Chinese Acad Sci Shanghai Microsyst & Informat Technol Res Inst Shanghai 200050 Peoples R China

For real-time multicast services over wireless multihop networks, to minimize the energy of transmissions with satisfying the requirements of a fixed data rate and high reliabilities, we construct a conflict graph based framework by joint optimizing network coding and scheduling. Then, we propose a primal-dual subgradient optimization algorithm by random sampling K maximal stable sets in a given conflict graph. This method transforms the NP-hard scheduling subproblem into a normal linear programming problem to obtain an approximate solution. The proposed algorithm only needs to adopt centralized technique for solving the linear programming problem while all of the other computations can be distributed. The simulation results show that, comparing with the existing algorithm, this algorithm can not only achieve about 20% performance gain, but also have better performance in terms of convergence and robustness.

关键词： REAL-time computing MULTICASTING (Computer networks) linear network coding SCHEDULING MATHEMATICAL optimization COMPUTER algorithms

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