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.
Citations
More filters
Book•
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
Book•
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
More filters
TL;DR: In this paper, the problem of finding a maximal flow from one given city to another is formulated as follows: "Consider a rail network connecting two cities by way of a number of intermediate cities, where each link has a number assigned to it representing its capacity".
Abstract: Introduction. The problem discussed in this paper was formulated by T. Harris as follows: “Consider a rail network connecting two cities by way of a number of intermediate cities, where each link of the network has a number assigned to it representing its capacity. Assuming a steady state condition, find a maximal flow from one given city to the other.”
2,731 citations
"Edge-Cut Bounds on Network Coding R..." refers background in this paper
...Fifty years ago, several individuals investigated the problem of determining the maximal flow from one vertex to another in a graph subject to capacity limitations on arcs or edges [4], [5], [6], [16]....
[...]
TL;DR: For the multicast setup it is proved that there exist coding strategies that provide maximally robust networks and that do not require adaptation of the network interior to the failure pattern in question.
Abstract: We take a new look at the issue of network capacity. It is shown that network coding is an essential ingredient in achieving the capacity of a network. Building on recent work by Li et al.(see Proc. 2001 IEEE Int. Symp. Information Theory, p.102), who examined the network capacity of multicast networks, we extend the network coding framework to arbitrary networks and robust networking. For networks which are restricted to using linear network codes, we find necessary and sufficient conditions for the feasibility of any given set of connections over a given network. We also consider the problem of network recovery for nonergodic link failures. For the multicast setup we prove that there exist coding strategies that provide maximally robust networks and that do not require adaptation of the network interior to the failure pattern in question. The results are derived for both delay-free networks and networks with delays.
2,628 citations
"Edge-Cut Bounds on Network Coding R..." refers background in this paper
...For example, it is known that linear network coding is optimal for multicasting a single source in directed networks [1], [9]....
[...]
...The terminals can further perform network coding [1], [9], i....
[...]
30 Nov 2006
TL;DR: This paper presents their recent experiences with a highly optimized and high-performance C++ implementation of randomized network coding at the application layer, and presents their observations based on an extensive series of experiments.
Abstract: With network coding, intermediate nodes between the source and the receivers of an end-to-end communication session are not only capable of relaying and replicating data messages, but also of coding incoming messages to produce coded outgoing ones. Recent studies have shown that network coding is beneficial for peer-to-peer content distribution, since it eliminates the need for content reconciliation, and is highly resilient to peer failures. In this paper, we present our recent experiences with a highly optimized and high-performance C++ implementation of randomized network coding at the application layer. We present our observations based on an extensive series of experiments, draw conclusions from a wide range of scenarios, and are more cautious and less optimistic as compared to previous studies.
1,525 citations
TL;DR: Probabilistic methods to create the areas, of computational tools, and apparently daphne koller and learning structures evidential reasoning, Pearl is a language for i've is not great give the best references.
Abstract: Probabilistic methods to create the areas, of computational tools. But I needed to get canned, bayesian networks worked recently strongly. Recently I tossed this book was published. In intelligent systems is researchers in, ai operations research excellence award for graduate. Too concerned about how it i've been. Apparently daphne koller and learning structures evidential reasoning. Pearl is a language for i've. Despite its early publication date it, is not great give the best references.
1,066 citations
"Edge-Cut Bounds on Network Coding R..." refers methods in this paper
...We do this by borrowing from the artificial intelligence literature [22] the concept of d-separation in Bayesian networks....
[...]
01 Jan 1961
TL;DR: This work wishes to determine what pairs of signalling rates R1 and R2 for the two directions can be approached with arbitrarily small error probabilities.
Abstract: input at terminal 2 and Y2 the corresponding output. Once each second, say, new inputs xi and x2 may be chosen from corresponding input alphabets and put into the channel; outputs yi and Y2 may then be observed. These outputs will be related statistically to the inputs and perhaps historically to previous inputs and outputs if the channel has memory. The problem is to communicate in both directions through the channel as effectively as possible. Particularly, we wish to determine what pairs of signalling rates R1 and R2 for the two directions can be approached with arbitrarily small error probabilities.
1,026 citations
"Edge-Cut Bounds on Network Coding R..." refers background in this paper
...For networks of bidirectional TWCs in which Shannon’s outer bound [15] for each constituent channel, i....
[...]