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Subspace Packings – Constructions and Bounds

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arXiv 2019年

作者： Etzion, Tuvi Kurz, Sascha Otal, Kamil Özbudak, Ferruh Computer Science Department Technion Haifa3200003 Israel University of Bayreuth Bayreuth Germany TÜBITAK BILGEM UEKAE Gebze Turkey Middle East Technical University Ankara Turkey

The Grassmannian Gq(n, k) is the set of all k-dimensional subspaces of the vector space Fnq . Kötter and Kschischang showed that codes in Grassmannian space can be used for error-correction in random network coding. On the other hand, these codes are q-analogs of codes in the Johnson scheme, i.e. constant dimension codes. These codes of the Grassmannian Gq(n, k) also form a family of q-analogs of block designs and they are called subspace designs. In this paper, we examine one of the last families of q-analogs of block designs which was not considered before. This family called subspace packings is the q-analog of packings, and was considered recently for network coding solution for a family of multicast networks called the generalized combination networks. A subspace packing t-(n, k, λ)q is a set S of k-subspaces from Gq(n, k) such that each t-subspace of Gq(n, t) is contained in at most λ elements of S. The goal of this work is to consider the largest size of such subspace packings. We derive a sequence of lower and upper bounds on the maximum size of such packings, analyse these bounds, and identify the important problems for further research in this *** Codes 94B65, 94B60, 51E20 Copyright © 2019, The Authors. All rights reserved.

关键词： network coding

network Coded Cooperative Multicast in Integrated Terrestrial-Satellite networks

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Network Coded Cooperative Multicast in Integrated Terrestria...

IEEE Symposium on Computers and Communications (ISCC)

作者： Xinmu Wang Hewu Li Mingkai Tong Kang Pan Qian Wu Department of Computer Science and Technology Tsinghua University Beijing China Institute for Network Sciences and Cyberspace Tsinghua University Beijing China

Wireless services have been extended from connection-centric to content-centric and this brings rapid increasing data traffic. Considering the concurrent multiple requests for popular contents, multicast is a promising delivery scheme to exploit content reuse. Satellite multicast is superior to others due to the coverage. When terrestrial base stations (BSs) are integrated with the satellite, cooperative transmission is then enabled to handle the fading satellite channels as well as maximize data throughput. Therefore, this paper proposes a co-operative multicast scheme for content delivery in the integrated terrestrial-satellite networks (ITSN) which is further enhanced by network coding. To exploit bandwidth of both terrestrial base stations (BSs) and the satellite, this cooperative multicast scheme uses two-phase transmission. The satellite multicast contents to subscribers in an opportunistic manner with real-time data rate adaptation. Then terrestrial BSs retransmit the lost packets for reliable transmission. Ground users are allocated to subgroups for the channel diversities while network coding is applied to packet loss recovery with fewer retransmissions. Sufficient numerical results demonstrate the enhancement on network throughput brought by the cooperative multicast scheme.

关键词： Satellite broadcasting Throughput network coding Interference Satellites Signal to noise ratio Fading channels

Finite-length performance comparison of network codes using random vs Pascal matrices

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arXiv 2019年

作者： Do-Duy, Tan Ángeles Vázquez-Castro, M. Department of Computer and Communication Engineering HCMC University of Technology and Education Viet Nam Department of Telecommunications and Systems Engineering School of Engineering Autonomous University of Barcelona Spain

In this letter, we evaluate the finite-length performance of network coding when using either random or structured encoding matrices. First, we present our novel construction of structured network codes over Fq (q = 2m) using Pascal matrices. We present their encoding, re-encoding and decoding in matrix notation and derive their packet loss rate. Second, we propose a novel methodology to compute the optimal finite-length coding rate for representative and realistic traffic applications. Finally, our method allows to compare the performance of our codes with the performance of popular random codes. We show that our constructions always have better throughput and minimal overhead, which is more significant for short code lengths. Further, their larger decoding delay fulfils the delay constraints of realistic scenarios (e.g. 5G multihop networks). Copyright © 2019, The Authors. All rights reserved.

关键词： network coding

Density Encoding Enables Resource-Efficient Randomly Connected Neural networks

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arXiv 2019年

作者： Kleyko, Denis Kheffache, Mansour Frady, E. Paxon Wiklund, Urban Osipov, Evgeny The Redwood Center for Theoretical Neuroscience The University of California BerkeleyCA94720 United States Intelligent Systems Lab Research Institutes of Sweden Kista164 40 Sweden Netlight Consulting AB Stockholm111 53 Sweden The Department of Radiation Sciences Biomedical Engineering Umeå University Umeå901 87 Sweden The Department of Computer Science Electrical and Space Engineering Luleå University of Technology Luleå971 87 Sweden

The deployment of machine learning algorithms on resource-constrained edge devices is an important challenge from both theoretical and applied points of view. In this article, we focus on resource-efficient randomly connected neural networks known as Random Vector Functional Link (RVFL) networks since their simple design and extremely fast training time make them very attractive for solving many applied classification tasks. We propose to represent input features via the density-based encoding known in the area of stochastic computing and use the operations of binding and bundling from the area of hyperdimensional computing for obtaining the activations of the hidden neurons. Using a collection of 121 real-world datasets from the UCI Machine Learning Repository, we empirically show that the proposed approach demonstrates higher average accuracy than the conventional RVFL. We also demonstrate that it is possible to represent the readout matrix using only integers in a limited range with minimal loss in the accuracy. In this case, the proposed approach operates only on small n-bits integers, which results in a computationally efficient architecture. Finally, through hardware Field-Programmable Gate Array (FPGA) implementations, we show that such an approach consumes approximately eleven times less energy than that of the conventional RVFL. © 2019, CC BY.

关键词： network coding

Hamming and simplex codes for the sum-rank metric

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arXiv 2019年

作者： Martínez-Peñas, Umberto Dept. of Electrical & Computer Engineering University of Toronto Canada

Sum-rank Hamming codes are introduced in this work. They are essentially defined as the longest codes with minimum sum-rank distance at least 3 for a fixed redundancy r, base-field size q and field-extension degree m (i.e., number of matrix rows). General upper bounds on their code length, number of shots or sublengths and average sublength are obtained based on such parameters. When the field-extension degree is 1, it is shown that sum-rank isometry classes of sum-rank Hamming codes are in bijective correspondence with maximal-size partial spreads. In that case, it is also shown that sum-rank Hamming codes are perfect codes for the sum-rank metric. Also in that case, estimates on the parameters of sum-rank Hamming codes are given, together with an efficient syndrome decoding algorithm. Duals of sum-rank Hamming codes, called sum-rank simplex codes, are then introduced. Bounds on the minimum sum-rank distance of sum-rank simplex codes are given based on known bounds on the size of partial spreads. As applications, sum-rank Hamming codes are proposed for error correction in multishot matrix-multiplicative channels and to construct locally repairable codes over small fields, including binary.94B05, 94B35, 94B65 Copyright © 2019, The Authors. All rights reserved.

关键词： network coding

Tunable Expansion Packets for Fulcrum codes

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Tunable Expansion Packets for Fulcrum codes

European Wireless Conference

作者： Vu Nguyen Elif Tasdemir Giang T. Nguyen Daniel E. Lucani Frank H. P. Fitzek

ISBN: (纸本)9783800749485

Fulcrum combines two encoding stages, first using one high Galois field, such as GF(2~8) and then with the binary Galois field GF(2). This allows intermediate and end devices, depending their computation power, to select either field to recode and decode coded packets. To ensure a high decoding probability, Fulcrum codes introduce r expansion packets at the outer coding stage, to increase the chance of producing linearly independent packets. However, the fixed number r hinder the chance of obtaining both high decoding probability and efficient transmission at a reduced computation complexity. We propose tunable expansion packet (TEP) protocols, which adjust the extra coefficients in the outer coding stage based on feedback from receivers. Comprehensive evaluations show that TEP protocols significantly increase goodput and reduce computation complexity while maintaining a low overhead.

关键词： network coding Fulcrum codes Heterogeneous devices Tunable coding Computation complexity

C-RAN-Assisted Non-Coherent Grant-Free Random Access Based on Compute-and-Forward

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C-RAN-Assisted Non-Coherent Grant-Free Random Access Based o...

IEEE Global Telecommunications Conference (GC Wkshps)

作者： Raceala-Motoc, Miruna Jung, Peter Utkovski, Zoran Stanczak, Slawomir Fraunhofer Heinrich Hertz Inst Berlin Germany Tech Univ Berlin Berlin Germany

ISBN: (纸本)9781538649206

Reliable communication in massive random access scenarios with short packet transmissions requires integration of novel network architecture solutions and multiple access methods. In this paper, we study the performance of an uncoordinated, grant-free random access scheme based on compute-and-forward (CoF) in a dense cloud radio access network (C-RAN) where multiple access points (out-of-band relays or radio units) are connected by low-rate links to a central processing instance. The access points decode linear equations of transmitted messages and forward these to the central processing instance, which solves for the original messages. In the context of the C-RAN architecture, the approach provides efficient utilization of the (limited) fronthaul resources, thus presenting an alternative to conventional C-RAN implementations. The performance of the CoF-based scheme is assessed in a realistic scenario where neither the transmit nor the receive instances have a priori channel state information (CSI). In our approach, pilot signals and data are transmitted in the same message, which meets a strong need for the integration of control and data for short message transmissions. An important aspect that we study is the trade-off between the resource allocation for reliable channel estimation and encoded data transmission given a reliability target.

关键词： Random Access Channel Estimation network coding Compute-and-Forward Quasi-Static Fading Short Codes LDPC Codes Practical coding Compressed Sensing

Performance of network coding enabled diversity relay networks

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Performance of network coding enabled diversity relay networ...

2012 5th International Conference on Advanced Technologies for Communications, ATC 2012

作者： Sinh, Cong Lam Quoc, Tuan Nguyen Duhamel, Pierre VNU University of Engineering and Technology E3 144 Xuan thuy Cau Giay Hanoi Viet Nam France

ISBN: (纸本)9781467343527

Cooperative network coding is considered as a novel technology that integrates cooperative communications with network coding to improve the throughput and robustness of the network. In this paper, a network coding enabled cooperative network with multiple relays is considered, under Rayleigh fading. The outage probability of this network is analyzed and showed to be superior to the traditional network with multiple relays. © 2012 IEEE.

关键词： network coding

Energy efficient authentication strategies for network coding

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Energy efficient authentication strategies for network codin...

作者： Apavatjrut, Anya Znaidi, Wassim Fraboulet, Antoine Goursaud, Claire Jaffrès-Runser, Katia Lauradoux, Cédric Minier, Marine Université de Lyon INRIA INSA-Lyon F-69621 Villeurbanne France

Recent advances in information theory and networking, e.g. aggregation, network coding or rateless codes, have significantly modified data dissemination in wireless networks. These new paradigms create new threats for security such as pollution attacks and denial of services (DoS). These attacks exploit the difficulty to authenticate data in such contexts. The particular case of xor network coding is considered herein. We investigate different strategies based on message authentication codes algorithms (MACs) to thwart these attacks. Yet, classical MAC designs are not compatible with the linear combination of network coding. Fortunately, MACs based on universal hash functions (UHFs) match nicely the needs of network coding: some of these functions are linear h(x 1⊕x2) = h(x1)⊕h(x2). To demonstrate their efficiency, we consider the case of wireless sensor networks (WSNs). Although these functions can drastically reduce the energy consumption of authentication (up to 68% gain over the classical designs is observed), they increase the threat of DoS. Indeed, an adversary can disrupt all communications by polluting few messages. To overcome this problem, a group testing algorithm is introduced for authentication resulting in a complexity linear in the number of attacks. The energy consumption is analyzed for cross-point and butterfly network topologies with respect to the possible attack scenarios. The results highlight the trade-offs between energy efficiency, authentication and the effective throughput for the different MAC modes. Copyright © 2011 John Wiley & Sons, Ltd.

关键词： network coding