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On Base Field of Linear network coding

IEEE TRANSACTIONS ON INFORMATION THEORY 2016年第12期62卷 7272-7282页

作者： Sun, Qifu Tyler Li, Shuo-Yen Robert Li, Zongpeng Univ Sci & Technol Beijing Sch Comp & Commun Engn Beijing 100083 Peoples R China Univ Elect Sci & Technol China Chengdu 611731 Peoples R China Univ Calgary Dept Comp Sci Calgary AB T2N 1N4 Canada Wuhan Univ Dept Comp Wuhan 430072 Hubei Peoples R China

For a (single-source) multicast network, the size of a base field is the most known and studied algebraic identity that is involved in characterizing its linear solvability over the base field. In this paper, we design a new class N of multicast networks and obtain an explicit formula for the linear solvability of these networks, which involves the associated coset numbers of a multiplicative subgroup in a base field. The concise formula turns out to be the first that matches the topological structure of a multicast network and algebraic identities of a field other than size. It further facilitates us to unveil infinitely many new multicast networks linearly solvable over GF(q) but not over GF(q') with q < q', based on a subgroup order criterion. In particular: 1) for every k >= 2, an instance in Al can be found linearly solvable over GF(2(2k)) but not over GF(2(2k+1)) and 2) for arbitrary distinct primes p and pc there are infinitely many k and k' such that an instance in Al can be found linearly solvable over GF(p(k)) but not over GF(p'(k)') with p(k) < p'(k)'.

关键词： network coding multicast network multiplicative subgroup coset generalized Cauchy-Davenport theorem

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Design and Analysis of Heterogeneous Physical Layer network coding

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IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS 2016年第4期15卷 2484-2497页

作者： Zhang, Haoyuan Zheng, Lei Cai, Lin Univ Victoria Dept Elect & Comp Engn Victoria BC V8W 3P6 Canada

In this paper, physical layer network coding with heterogeneous modulations (HePNC) is proposed for the asymmetric two-way relay channel (TWRC) scenario. The existing PNC solutions using the same modulation for signals transmitted from two source nodes may not be desirable for practical situations when traffic loads exchanged between the sources are unequal and channel conditions of source-relay links are heterogeneous. HePNC includes two stages: multiple access (MA) and broadcast (BC) stages. In the MA stage, the two source nodes transmit to the relay simultaneously with heterogeneous modulations selected according to the channel conditions and the ratio of traffic loads exchanged between the sources, and then the signals superimposed at the relay are mapped to a network-coded symbol by a mapping function adaptively;in the BC stage, the relay broadcasts the network-coded symbol back to both sources with a modulation selected according to the bottleneck link's channel condition. We present three HePNC designs, including QPSK-BPSK, 8PSK-BPSK and 16QAM-BPSK HePNC. How to design and optimize the mapping function is investigated and the error performance of QPSK-BPSK HePNC is analyzed. We further study the HePNC system performance, throughput upper bound and energy efficiency. Extensive simulations demonstrated that the proposed HePNC can substantially enhance the throughput and energy efficiency compared with the existing PNC.

关键词： Relays network coding Binary phase shift keying System performance Throughput Synchronization

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Alignment-Based network coding for Two-Unicast-Z networks

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IEEE TRANSACTIONS ON INFORMATION THEORY 2016年第6期62卷 3183-3211页

作者： Zeng, Weifei Cadambe, Viveck R. Medard, Muriel MIT Elect Res Lab Cambridge MA 02139 USA Penn State Univ Dept Elect Engn University Pk PA 16802 USA

In this paper, we study the wireline two-unicast-Z communication network over directed acyclic graphs. The two-unicast-Z network is a two-unicast network where the destination intending to decode the second message has a priori side information of the first message. We make three contributions in this paper. First, we describe a new linear network coding algorithm for two-unicast-Z networks over the directed acyclic graphs. Our approach includes the idea of interference alignment as one of its key ingredients. For the graphs of a bounded degree, our algorithm has linear complexity in terms of the number of vertices, and the polynomial complexity in terms of the number of edges. Second, we prove that our algorithm achieves the rate pair (1, 1) whenever it is feasible in the network. Our proof serves as an alternative, albeit restricted to two-unicast-Z networks over the directed acyclic graphs, to an earlier result of Wang et al., which studied the necessary and sufficient conditions for the feasibility of the rate pair (1, 1) in two-unicast networks. Third, we provide a new proof of the classical max-flow min-cut theorem for the directed acyclic graphs.

关键词： Linear codes network coding dynamic programming heuristic algorithms

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Linear network coding, Linear Index coding and Representable Discrete Polymatroids

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IEEE TRANSACTIONS ON INFORMATION THEORY 2016年第7期62卷 4096-4119页

作者： Muralidharan, Vijayvaradharaj Tirucherai Rajan, B. Sundar Indian Inst Sci Dept Elect Commun Engn Bengaluru 560012 Karnataka India Qualcomm India Private Ltd Hyderabad 500081 Andhra Pradesh India

Discrete polymatroids are the multi-set analogue of matroids. In this paper, we explore the connections among linear network coding, linear index coding, and representable discrete polymatroids. We consider the vector linear solutions of networks over a field F-q, with possibly different message and edge vector dimensions, which are referred to as linear fractional solutions. It is well known that a scalar linear solution over F-q exists for a network if and only if the network is matroidal with respect to a matroid representable over F-q. We define a discrete polymatroidal network and show that a linear fractional solution over a field F-q exists for a network if and only if the network is discrete polymatroidal with respect to a discrete polymatroid representable over F-q. An algorithm to construct the networks starting from certain class of discrete polymatroids is provided. Every representation over F-q for the discrete polymatroid, results in a linear fractional solution over F-q for the constructed network. Next, we consider the index coding problem, which involves a sender, which generates a set of messages X = {x(1), x(2),... x(k)}, and a set of receivers R, which demand messages. A receiver R is an element of R is specified by the tuple (x, H), where x. X is the message demanded by R and H subset of X\{x} is the side information possessed by R. We first show that a linear solution to an index coding problem exists if and only if there exists a representable discrete polymatroid, satisfying certain conditions, which are determined by the index coding problem considered. Rouayheb et al. showed that the problem of finding a multi-linear representation for a matroid can be reduced to finding a perfect linear index coding solution for an index coding problem obtained from that matroid. The multi-linear representation of a matroid can be viewed as a special case of representation of an appropriate discrete polymatroid. We generalize the result of Rouayheb et al.,

关键词： Index coding matroids network coding polymatroids

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Inter-Session network coding-Based Policies for Delay Tolerant Mobile Social networks

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IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS 2016年第11期15卷 7329-7342页

作者： Shrestha, Neetya Sassatelli, Lucile Univ Cote dAzur CNRS Lab Informat Signal Syst Sophia Antipolis F-06903 Sophia Antipolis France

We consider delay tolerant mobile social networks (DTMSNs), which are opportunistic networks made of human-carried wireless devices clustered into social communities. In such environments, routing is a challenge as the limited resources (such as memory and contact opportunities) must be efficiently used and shared between the sessions (or users, contents). To handle several unicast sessions, inter-session network coding (ISNC) has been proved necessary for optimal throughput in general networks, but is a delicate problem as it can quickly get detrimental. This paper investigates that ISNC can be beneficial to DTMSNs when used on top of a social-aware routing algorithm, whereas we exemplify and make explicit why any gain can hardly be expected with greedy replication, in regard to the current literature on ISNC. We then design decentralized criteria to control when and where in the network ISNC should be triggered, based on the node features (buffer size and social relationships) and network current load. These criteria are tested extensively on real-world contact traces, in terms of various metrics, such as number of deliveries, mean delay, or fairness. Our online ISNC protocol builds on the SimBet utility-routing policy. Our ISNC protocol can, however, run on top of any social-aware routing.

关键词： Wireless networks disruption tolerant networking network coding

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Security Analysis and Improvement of a Tag Encoding Authentication Scheme for network coding

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Wuhan University Journal of Natural Sciences 2016年第5期21卷 394-398页

作者： LIU Guangjun School of Information Engineering Xi'an University

A tag encoding authentication scheme for network coding proposed by Wu et al was claimed to defend pollution attacks efficiently. However, we find that the scheme easily incurs multi-generation pollution attacks, where an adversary may be able to recover the main secret key of the source with high probability during multi-generation transmitting, and the scheme also cannot resist against inter-generation pollution attacks. Using a dynamic source secret key technology that the key can be updated with the change of generation identifier, an improved scheme is then presented, which can counteract these security defects without any efficiency compromise.

关键词： network coding pollution attack inter-generation pollution attack multi-generation pollution attack

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Best of Both Worlds: Prioritizing network coding Without Increased Space Complexity 41

Best of Both Worlds: Prioritizing Network Coding Without Inc...

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41st IEEE Conference on Local Computer networks (LCN)

作者： Naumann, Roman Dietzel, Stefan Scheuermann, Bjoern Humboldt Univ Berlin Germany

ISBN: (纸本)9781509020546

Random linear network coding simplifies routing decisions, improves throughput, and increases tolerance against packet loss. A substantial limitation, however, is delay: decoding requires as many independent linear combinations as data blocks. Hierarchical network coding purportedly solves this delay problem. It introduces layers to decode prioritized data blocks early, which may benefit video streaming applications or applications for sensor information collection. While hierarchical network coding reduces decoding delays, it introduces significant space complexity and additional decoding time. We propose a decoding algorithm that manages all prioritization layers in a joint decoder matrix. Analytical evaluation and performance measurements show that we maintain prioritization benefits without increased space complexity and improve decoding performance. With memory requirements independent of the number of layers, our algorithm facilitates more fine-grained prioritization layers to further the benefits of hierarchical network coding.

关键词： network coding random linear network coding hierarchical network coding prioritization decoding

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Pollution Attack Resistance Dissemination in VANETs Based on network coding 7

Pollution Attack Resistance Dissemination in VANETs Based on...

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7th International Conference on Ambient Systems, networks and Technologies (ANT) / 6th International Conference on Sustainable Energy Information Technology (SEIT)

作者： Wu, Guowei Wang, Jie Wang, Yongchuan Yao, Lin Dalian Univ Technol Sch Software Dalian 116621 Peoples R China Wuhan Econ & Technol Dev Zone 531 Jiangcheng Ave Wuhan 430056 Peoples R China

network coding is widely used in the dissemination schemes of VANETs, because it can improve the network throughput. However, it will bring the pollution attack into the network, making the decoding procedure error, so vehicles can not recover the original file. Therefore, we need adopt a signature scheme to validate a piece without decoding. In the current signing schemes, the linear subspace signature scheme is to defend the pollution attack. But the length of the signature equal to the piece size required several packets to be transmitted together. Moreover, even one lost packet or polluted packet may make the whole piece dropped including the unpolluted packets, causing the limited resources to be wasted. In this paper, we adopt the padding scheme, obtain a packet-size vector which is orthogonal to linear space spanned by all packets in a generation and sign the vector, reducing the length of the signature into packet size and more importantly validating coded packets other than coded pieces in a generation. The simulation shows that our scheme has higher downloading rate, and lower downloading delay. (C) 2016 The Authors. Published by Elsevier B.V.

关键词： VANET dissemination pollution attack network coding

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On the Benefits of network coding for Unicast Application in Opportunistic Traffic Offloading 2

On the Benefits of Network Coding for Unicast Application in...

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2nd International Conference on Fuzzy Systems and Data Mining (FSDM)

作者： Jiao, Jia-Ke Pan, Da-Ru Lv, Ke Sun, Li-Fen South China Normal Univ Sch Phys & Telecommun Engn Guangzhou Guangdong Peoples R China Univ Chinese Acad Sci Beijing Peoples R China

ISBN: (纸本)9781614997221;9781614997214

With the explosive increase in mobile services and user demands, cellular networks will very likely be overloaded and congested in the near future. To cope with this explosive growth in traffic demands with the limited current network capacity, opportunistic network is used to offload traffic from cellular networks to free device-to-device networks. network coding can make full use of the mobility of nodes and improve the performance of opportunistic traffic offloading. In this paper, we investigate the benefits of applying a form of network coding known as random linear coding to unicast application in opportunistic traffic offloading. Moreover we establish a mathematical model to analyze the benefits of RLC. RLC schemes achieve faster information propagation at the price of a greater number of transmissions and take up a lot of storage space. To optimize scheme, we utilize the survival time to control the number of packets in the network and free up storage space for node.

关键词： Opportunistic network network coding packets control

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Linear Physical-layer network coding for the Fading Y-channel without Transmitter Channel State Information 84

Linear Physical-layer Network Coding for the Fading Y-channe...

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84th IEEE Vehicular Technology Conference (VTC-Fall)

作者： Guo, Jiajia Yang, Tao Yuan, Jinhong Zhang, Jian A. Univ New South Wales Sydney NSW Australia Univ Technol Sydney Sydney NSW Australia CSIRO Data61 Sydney NSW Australia

ISBN: (纸本)9781509017010

In this paper, we propose a new linear physical-layer network coding (NC) scheme for the fading Y-channel, assuming that the channel state information (CSI) is not available at transmitters. In this scheme, each user transmits one message to a relay and intends to obtain both other two users' messages. Based on the receiver-side CSI, the relay determines two NC generator vectors for linear network coding, and reconstructs the associated two linear NC codewords. For the case when there is one time-slot in the uplink phase, we present an explicit solution for the generator vectors that minimizes the error probability at a high SNR, and a lower bound of the error performance of the proposed scheme using our optimized generator vectors. Extending to multiple time-slots in the uplink, two typical scenarios are discussed. Numerical results show that the proposed scheme significantly outperforms existing schemes, and match well with our analytical results.

关键词： Relays Uplink Generators Error probability network coding Silicon Fading channels network coding Error probability relay up link dynamos Fading channels Silicon Transmitters error performance Explicit Solution Channel state information hierarchical network high SNR

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