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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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
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01 Jan 2003
TL;DR: A success probability bound is obtained for randomized network coding in link-redundant networks with unreliable links, in terms of link failure probability and amount of redundancy.
Abstract: We consider a randomized network coding approach for multicasting from several sources over a network, in which nodes independently and randomly select linear mappings from inputs onto output links over some field. This approach was first described in [3], which gave, for acyclic delay-free networks, a bound on error probability, in terms of the number of receivers and random coding output links, that decreases exponentially with code length. The proof was based on a result in [2] relating algebraic network coding to network flows. In this paper, we generalize these results to networks with cycles and delay. We also show, for any given acyclic network, a tighter bound in terms of the probability of connection feasibility in a related network problem with unreliable links. From this we obtain a success probability bound for randomized network coding in link-redundant networks with unreliable links, in terms of link failure probability and amount of redundancy.
608 citations
TL;DR: The main result is a theorem: the maximum possible flow from left to right through a network is equal to the minimum value among all simple cut-sets.
Abstract: This note discusses the problem of maximizing the rate of flow from one terminal to another, through a network which consists of a number of branches, each of which has a limited capacity. The main result is a theorem: The maximum possible flow from left to right through a network is equal to the minimum value among all simple cut-sets. This theorem is applied to solve a more general problem, in which a number of input nodes and a number of output nodes are used.
493 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]....
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24 Oct 2004
TL;DR: This paper shows that under a simplified layered model of wireless networks, the minimum-energy multicast problem in mobile ad hoc networks is solvable as a linear program, assuming network coding.
Abstract: The minimum energy required to transmit one bit of information through a network characterizes the most economical way to communicate in a network. In this paper, we show that, under a layered model of wireless networks, the minimum energy-per-bit for multicasting in a mobile ad hoc network can be found by a linear program; the minimum energy-per-bit can be attained by performing network coding. Compared with conventional routing solutions, network coding not only allows a potentially lower energy-per-bit to be achieved, but also enables the optimal solution to be found in polynomial time, in sharp contrast with the NP-hardness of constructing the minimum-energy multicast tree as the optimal routing solution. We further show that the minimum energy multicast formulation is equivalent to a cost minimization with linear edge-based pricing, where the edge prices are the energy-per-bits of the corresponding physical broadcast links. This paper also investigates minimum energy multicasting with routing. Due to the linearity of the pricing scheme, the minimum energy-per-bit for routing is achievable by using a single distribution tree. A characterization of the admissible rate region for routing with a single tree is presented. The minimum energy-per-bit for multicasting with routing is found by an integer linear program. We show that the relaxation of this integer linear program, studied earlier in the Steiner tree literature, can now be interpreted as the optimization for minimum energy multicasting with network coding. In short, this paper presents a unifying study of minimum energy multicasting with network coding and routing.
404 citations
01 Jan 1998
374 citations
"Edge-Cut Bounds on Network Coding R..." refers background in this paper
...FDGs are graphs where the vertices represent random variables, and the edges represent the functional dependencies between the random variables [10], [11]....
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IBM1
TL;DR: In this paper, the authors generalize the max-flow min-cut theorem of Ford and Fulkerson to the problem of finding the maximum simultaneous flows of two commodities and give an algorithm similar to the labelling method for constructing the two flows.
Abstract: A network is a set of nodes Ni connected by arcs with nonnegative arc capacities bij which indicates the maximum amount of flow that can pass through the arc from Ni to Nj. Given all bij, there is a maximum flow from Ni to Nj using all arcs. Under the assumption that bij = bji, the present paper generalizes the max-flow min-cut theorem of Ford and Fulkerson to the problem of finding the maximum simultaneous flows of two commodities and gives an algorithm similar to the labelling method for constructing the two flows.
374 citations