Edge-Cut Bounds on Network Coding Rates
TL;DR: A new bound on communication rates is developed that applies to network coding, which is a promising active network application that has processors transmit packets that are general functions, for example a bit-wise XOR of selected received packets.
Abstract: Active networks are network architectures with processors that are capable of executing code carried by the packets passing through them. A critical network management concern is the optimization of such networks and tight bounds on their performance serve as useful design benchmarks. A new bound on communication rates is developed that applies to network coding, which is a promising active network application that has processors transmit packets that are general functions, for example a bit-wise XOR, of selected received packets. The bound generalizes an edge-cut bound on routing rates by progressively removing edges from the network graph and checking whether certain strengthened d-separation conditions are satisfied. The bound improves on the cut-set bound and its efficacy is demonstrated by showing that routing is rate-optimal for some commonly cited examples in the networking literature.
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16 Jan 2012TL;DR: In this article, a comprehensive treatment of network information theory and its applications is provided, which provides the first unified coverage of both classical and recent results, including successive cancellation and superposition coding, MIMO wireless communication, network coding and cooperative relaying.
Abstract: This comprehensive treatment of network information theory and its applications provides the first unified coverage of both classical and recent results. With an approach that balances the introduction of new models and new coding techniques, readers are guided through Shannon's point-to-point information theory, single-hop networks, multihop networks, and extensions to distributed computing, secrecy, wireless communication, and networking. Elementary mathematical tools and techniques are used throughout, requiring only basic knowledge of probability, whilst unified proofs of coding theorems are based on a few simple lemmas, making the text accessible to newcomers. Key topics covered include successive cancellation and superposition coding, MIMO wireless communication, network coding, and cooperative relaying. Also covered are feedback and interactive communication, capacity approximations and scaling laws, and asynchronous and random access channels. This book is ideal for use in the classroom, for self-study, and as a reference for researchers and engineers in industry and academia.
2,442 citations
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01 Jun 2007TL;DR: This article reviews progress in cooperative communication networks and intends its presentation to be a tutorial for the reader who is familiar with information theory concepts but has not actively followed the field.
Abstract: This article reviews progress in cooperative communication networks. Our survey is by no means exhaustive. Instead, we assemble a representative sample of recent results to serve as a roadmap for the area. Our emphasis is on wireless networks, but many of the results apply to cooperation in wireline networks and mixed wireless/wireline networks. We intend our presentation to be a tutorial for the reader who is familiar with information theory concepts but has not actively followed the field. For the active researcher, this contribution should serve as a useful digest of significant results. This article is meant to encourage readers to find new ways to apply the ideas of network cooperation and should make the area sufficiently accessible to network designers to contribute to the advancement of networking practice.
334 citations
Book•
25 Jun 2008TL;DR: This survey builds up knowledge on random coding, binning, superposition coding, and capacity converses by introducing progressively more sophisticated tools for a selection of source and channel models.
Abstract: This survey reviews fundamental concepts of multi-user information theory. Starting with typical sequences, the survey builds up knowledge on random coding, binning, superposition coding, and capacity converses by introducing progressively more sophisticated tools for a selection of source and channel models. The problems addressed include: Source Coding; Rate-Distortion and Multiple Descriptions; Capacity-Cost; The Slepian–Wolf Problem; The Wyner-Ziv Problem; The Gelfand-Pinsker Problem; The Broadcast Channel; The Multiaccess Channel; The Relay Channel; The Multiple Relay Channel; and The Multiaccess Channel with Generalized Feedback. The survey also includes a review of basic probability and information theory.
290 citations
TL;DR: The Vamos network is constructed, and it is proved that Shannon-type information inequalities are insufficient even for computing network coding capacities of multiple-unicast networks.
Abstract: We define a class of networks, called matroidal networks, which includes as special cases all scalar-linearly solvable networks, and in particular solvable multicast networks. We then present a method for constructing matroidal networks from known matroids. We specifically construct networks that play an important role in proving results in the literature, such as the insufficiency of linear network coding and the unachievability of network coding capacity. We also construct a new network, from the Vamos matroid, which we call the Vamos network, and use it to prove that Shannon-type information inequalities are in general not sufficient for computing network coding capacities. To accomplish this, we obtain a capacity upper bound for the Vamos network using a non-Shannon-type information inequality discovered in 1998 by Zhang and Yeung, and then show that it is smaller than any such bound derived from Shannon-type information inequalities. This is the first application of a non-Shannon-type inequality to network coding. We also compute the exact routing capacity and linear coding capacity of the Vamos network. Finally, using a variation of the Vamos network, we prove that Shannon-type information inequalities are insufficient even for computing network coding capacities of multiple-unicast networks.
279 citations
Book•
01 Nov 2012TL;DR: 1. The concept of cognitive radio, capacity of cognitiveRadio networks, and Propagation issues for cognitive radio: a review.
Abstract: Widely regarded as one of the most promising emerging technologies for driving the future development of wireless communications, cognitive radio has the potential to mitigate the problem of increasing radio spectrum scarcity through dynamic spectrum allocation. Drawing on fundamental elements of information theory, network theory, propagation, optimisation and signal processing, a team of leading experts present a systematic treatment of the core physical and networking principles of cognitive radio and explore key design considerations for the development of new cognitive radio systems. Containing all the underlying principles you need to develop practical applications in cognitive radio, this book is an essential reference for students, researchers and practitioners alike in the field of wireless communications and signal processing.
236 citations
References
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31 May 2001
TL;DR: The basic active networking paradigm is introduced and its potential impacts on the future of information handling in general and on communications in particular are introduced.
Abstract: From the Publisher:
Active networking is an exciting new paradigm in digital networking that has the potential to revolutionize the manner in which communication takes place. It is an emerging technology, one in which new ideas are constantly being formulated and new topics of research are springing up even as this book is being written. This technology is very likely to appeal to a broad spectrum of users from academia and industry. Therefore, this book was written in a way that enables all these groups to understand the impact of active networking in their sphere of interest. Information services managers, network administrators, and e-commerce developers would like to know the potential benefits of the new technology to their businesses, networks, and applications. The book introduces the basic active networking paradigm and its potential impacts on the future of information handling in general and on communications in particular. This is useful for forward-looking businesses that wish to actively participate in the development of active networks and ensure a head start in the integration of the technology in their future products, be they applications or networks. Areas in which active networking is likely to make significant impact are identified, and the reader is pointed to any related ongoing research efforts in the area.
29 citations
01 Jan 2003
25 citations
"Edge-Cut Bounds on Network Coding R..." refers background or methods in this paper
...We shall discuss a strengthened version of this bound for undirected networks that is taken from [12]....
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...Instead, in [12] we employ an informationtheoretic cut-set bound that takes coding into account, and we summarize our results here....
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...We adopted in [13] the model of [2], [12] where the network is clocked, i....
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...We refer to [12] for more details on the remaining assumptions....
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...Such bounds clearly apply to undirected graphs, and one can prove this by using the techniques of [12]....
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31 Oct 2005
TL;DR: A bound on network coding rates is developed that generalizes an edge-cut bound on routing rates and is demonstrated by showing that routing is rate-optimal for some commonly cited examples in the networking literature.
Abstract: A bound on network coding rates is developed that generalizes an edge-cut bound on routing rates. The bound involves progressively removing edges from a network graph and checking whether certain strengthened d-separation conditions are satisfied. The bound improves on the cut-set bound, and its efficacy is demonstrated by showing that routing is rate-optimal for some commonly cited examples in the networking literature
18 citations
"Edge-Cut Bounds on Network Coding R..." refers background in this paper
...Some of the distinguishing features of our work are (see [ 33 ]): the PdE bound applies to general multimessage multicast, we have a formal procedure for generating rate bounds by using FDGs and d-separation (which makes a connection to the artificial intelligence literature), the progressive nature of our fd-separation bound strengthens an approach based on cutting edges only at the first step, and FDGs let us treat noisy networks as well ......
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09 Jul 2003
TL;DR: This is the first paper to the authors' knowledge that looks at network management for general connections, and gives bounds on the network management information needed for link failure recovery in various network connection problems, in terms of basic parameters such as the number of source processes and theNumber of links in a minimum source-receiver cut.
Abstract: We present an information theoretic framework for network management for recovery from nonergodic link failures. Building on recent work in the field of network coding, we describe the input-output relations of network nodes in terms of network codes. This very general concept of network behavior as a code provides a fundamental way to quantify essential management information as that needed to switch among different codes (behaviors) for different failure scenarios. We give bounds on the network management information needed for link failure recovery in various network connection problems, in terms of basic parameters such as the number of source processes and the number of links in a minimum source-receiver cut. This is the first paper to our knowledge that looks at network management for general connections.
17 citations
"Edge-Cut Bounds on Network Coding R..." refers background in this paper
...Among the contributions of [13] are bounds on management requirements for several network connection problems....
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