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863
XORs in the air: practical wireless network coding
- In Proc. ACM SIGCOMM
, 2006
"... This paper proposes COPE, a new architecture for wireless mesh networks. In addition to forwarding packets, routers mix (i.e., code) packets from different sources to increase the information content of each transmission. We show that intelligently mixing packets increases network throughput. Our de ..."
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Cited by 548 (20 self)
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This paper proposes COPE, a new architecture for wireless mesh networks. In addition to forwarding packets, routers mix (i.e., code) packets from different sources to increase the information content of each transmission. We show that intelligently mixing packets increases network throughput. Our design is rooted in the theory of network coding. Prior work on network coding is mainly theoretical and focuses on multicast traffic. This paper aims to bridge theory with practice; it addresses the common case of unicast traffic, dynamic and potentially bursty flows, and practical issues facing the integration of network coding in the current network stack. We evaluate our design on a 20-node wireless network, and discuss the results of the first testbed deployment of wireless network coding. The results show that COPE largely increases network throughput. The gains vary from a few percent to several folds depending on the traffic pattern, congestion level, and transport protocol.
Practical Network Coding
, 2003
"... We propose a distributed scheme for practical network coding that obviates the need for centralized knowledge of the graph topology, the encoding functions, and the decoding functions, and furthermore obviates the need for information to be communicated synchronously through the network. The resu ..."
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Cited by 462 (15 self)
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We propose a distributed scheme for practical network coding that obviates the need for centralized knowledge of the graph topology, the encoding functions, and the decoding functions, and furthermore obviates the need for information to be communicated synchronously through the network. The result is a practical system for network coding that is robust to random packet loss and delay as well as robust to any changes in the network topology or capacity due to joins, leaves, node or link failures, congestion, and so on. We simulate such a practical network coding system using the network topologies of several commercial Internet Service Providers, and demonstrate that it can achieve close to the theoretically optimal performance.
Fading relay channels: Performance limits and space-time signal design
- IEEE J. SELECT. AREAS COMMUN
, 2004
"... Cooperative diversity is a transmission technique where multiple terminals pool their resources to form a virtual antenna array that realizes spatial diversity gain in a distributed fashion. In this paper, we examine the basic building block of cooperative diversity systems, a simple fading relay ch ..."
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Cited by 445 (4 self)
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Cooperative diversity is a transmission technique where multiple terminals pool their resources to form a virtual antenna array that realizes spatial diversity gain in a distributed fashion. In this paper, we examine the basic building block of cooperative diversity systems, a simple fading relay channel where the source, destination and relay terminals are each equipped with single antenna transceivers. We consider three different TDMA-based cooperative protocols that vary the degree of broadcasting and receive collision. The relay terminal operates in either the amplify-and-forward (AF) or decode-and-forward (DF) modes. For each protocol, we study the ergodic and outage capacity behavior (assuming Gaussian code books) under the AF and DF modes of relaying. We analyze the spatial diversity performance of the various protocols and find that full spatial diversity (second-order in this case) is achieved by certain protocols provided that appropriate power control is employed. Our analysis unifies previous results reported in the literature and establishes the superiority (both from a capacity as well as a diversity point-of-view) of a new protocol proposed in this paper. The second part of the paper is devoted to (distributed) space-time code design for fading relay channels operating in the AF mode. We show that the corresponding code design criteria consist of the traditional rank and determinant criteria for the case of co-located antennas as well as appropriate power control rules. Consequently space-time codes designed for the case of co-located multi-antenna channels can be used to realize cooperative diversity provided that appropriate power control is employed.
The benefits of coding over routing in a randomized setting
- In Proceedings of 2003 IEEE International Symposium on Information Theory
, 2003
"... Abstract — We present a novel randomized coding approach for robust, distributed transmission and compression of information in networks. We give a lower bound on the success probability of a random network code, based on the form of transfer matrix determinant polynomials, that is tighter than the ..."
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Cited by 361 (44 self)
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Abstract — We present a novel randomized coding approach for robust, distributed transmission and compression of information in networks. We give a lower bound on the success probability of a random network code, based on the form of transfer matrix determinant polynomials, that is tighter than the Schwartz-Zippel bound for general polynomials of the same total degree. The corresponding upper bound on failure probability is on the order of the inverse of the size of the finite field, showing that it can be made arbitrarily small by coding in a sufficiently large finite field, and that it decreases exponentially with the number of codeword bits. We demonstrate the advantage of randomized coding over routing for distributed transmission in rectangular grid networks by giving, in terms of the relative grid locations of a source-receiver pair, an upper bound on routing success probability that is exceeded by a corresponding lower bound on coding success probability for sufficiently large finite fields. We also show that our lower bound on the success probability of randomized coding holds for linearly correlated sources. This implies that randomized coding effectively compresses linearly correlated information to the capacity of any network cut in a feasible connection problem. I.
Embracing wireless interference: Analog network coding
- in ACM SIGCOMM
, 2007
"... Traditionally, interference is considered harmful. Wireless networks strive to avoid scheduling multiple transmissions at the same time in order to prevent interference. This paper adopts the opposite approach; it encourages strategically picked senders to interfere. Instead of forwarding packets, r ..."
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Cited by 358 (10 self)
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Traditionally, interference is considered harmful. Wireless networks strive to avoid scheduling multiple transmissions at the same time in order to prevent interference. This paper adopts the opposite approach; it encourages strategically picked senders to interfere. Instead of forwarding packets, routers forward the interfering signals. The destination leverages network-level information to cancel the interference and recover the signal destined to it. The result is analog network coding because it mixes signals not bits. So, what if wireless routers forward signals instead of packets? Theoretically, such an approach doubles the capacity of the canonical relay network. Surprisingly, it is also practical. We implement our design using software radios and show that it achieves significantly higher throughput than both traditional wireless routing and prior work on wireless network coding. 1.
Network Coding for Distributed Storage Systems
, 2008
"... Distributed storage systems provide reliable access to data through redundancy spread over individually unreliable nodes. Application scenarios include data centers, peer-to-peer storage systems, and storage in wireless networks. Storing data using an erasure code, in fragments spread across nodes, ..."
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Cited by 338 (13 self)
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Distributed storage systems provide reliable access to data through redundancy spread over individually unreliable nodes. Application scenarios include data centers, peer-to-peer storage systems, and storage in wireless networks. Storing data using an erasure code, in fragments spread across nodes, requires less redundancy than simple replication for the same level of reliability. However, since fragments must be periodically replaced as nodes fail, a key question is how to generate encoded fragments in a distributed way while transferring as little data as possible across the network. For an erasure coded system, a common practice to repair from a node failure is for a new node to download subsets of data stored at a number of surviving nodes, reconstruct a lost coded block using the downloaded data, and store it at the new node. We show that this procedure is sub-optimal. We introduce the notion of regenerating codes, which allow a new node to download functions of the stored data from the surviving nodes. We show that regenerating codes can significantly reduce the repair bandwidth. Further, we show that there is a fundamental tradeoff between storage and repair bandwidth which we theoretically characterize using flow arguments on an appropriately constructed graph. By invoking constructive results in network coding, we introduce regenerating codes that can achieve any point in this optimal tradeoff.
Distributed Space-Time Coded Protocols for Exploiting Cooperative Diversity in Wireless Networks
- IEEE Trans. Inform. Theory
, 2003
"... Abstract — We develop and analyze space-time coded cooperative diversity protocols for combating multipath fading across multiple protocol layers in a wireless network. The protocols exploit spatial diversity available among a collection of distributed terminals that relay messages for one another i ..."
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Cited by 333 (10 self)
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Abstract — We develop and analyze space-time coded cooperative diversity protocols for combating multipath fading across multiple protocol layers in a wireless network. The protocols exploit spatial diversity available among a collection of distributed terminals that relay messages for one another in such a manner that the destination terminal can average the fading, even though it is unknown a priori which terminals will be involved. In particular, a source initiates transmission to its destination, and many relays potentially receive the transmission. Those terminals that can fully decode the transmission utilize a space-time code to cooperatively relay to the destination. We demonstrate that these protocols achieve full spatial diversity in the number of cooperating terminals, not just the number of decoding relays, and can be used effectively for higher spectral efficiencies than repetitionbased schemes. We discuss issues related to space-time code design for these protocols, emphasizing codes that readily allow for appealing distributed versions. I.
Trading structure for randomness in wireless opportunistic routing
, 2007
"... Opportunistic routing is a recent technique that achieves high throughput in the face of lossy wireless links. The current opportunistic routing protocol, ExOR, ties the MAC with routing, imposing a strict schedule on routers ’ access to the medium. Although the scheduler delivers opportunistic gain ..."
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Cited by 296 (7 self)
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Opportunistic routing is a recent technique that achieves high throughput in the face of lossy wireless links. The current opportunistic routing protocol, ExOR, ties the MAC with routing, imposing a strict schedule on routers ’ access to the medium. Although the scheduler delivers opportunistic gains, it misses some of the inherent features of the 802.11 MAC. For example, it prevents spatial reuse and thus may underutilize the wireless medium. It also eliminates the layering abstraction, making the protocol less amenable to extensions to alternate traffic types such as multicast. This paper presents MORE, a MAC-independent opportunistic routing protocol. MORE randomly mixes packets before forwarding them. This randomness ensures that routers that hear the same transmission do not forward the same packets. Thus, MORE needs no special scheduler to coordinate routers and can run directly on top of 802.11. Experimental results from a 20-node wireless testbed show that MORE’s median unicast throughput is 22 % higher than ExOR, and the gains rise to 45 % over ExOR when there is a chance of spatial reuse. For multicast, MORE’s gains increase with the number of destinations, and are 35-200 % greater than ExOR.
Wireless Network Information Flow: A Deterministic Approach
, 2009
"... In contrast to wireline networks, not much is known about the flow of information over wireless networks. The main barrier is the complexity of the signal interaction in wireless channels in addition to the noise in the channel. A widely accepted model is the the additive Gaussian channel model, and ..."
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Cited by 296 (42 self)
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In contrast to wireline networks, not much is known about the flow of information over wireless networks. The main barrier is the complexity of the signal interaction in wireless channels in addition to the noise in the channel. A widely accepted model is the the additive Gaussian channel model, and for this model, the capacity of even a network with a single relay node is open for 30 years. In this paper, we present a deterministic approach to this problem by focusing on the signal interaction rather than the noise. To this end, we propose a deterministic channel model which is analytically simpler than the Gaussian model but still captures two key wireless channel properties of broadcast and superposition. We consider a model for a wireless relay network with nodes connected by such deterministic channels, and present an exact characterization of the end-to-end capacity when there is a single source and one or more destinations (all interested in the same information) and an arbitrary number of relay nodes. This result is a natural generalization of the celebrated max-flow min-cut theorem for wireline networks. We then use the insights obtained from the analysis of the deterministic model to study information flow for the Gaussian wireless relay network. We present an achievable rate for general Gaussian relay networks and show that it is within a constant number of bits from the cut-set bound on the capacity of these networks. This constant depends on the number of nodes in the network, but not the values of the channel gains or the signal-to-noise ratios. We show that existing strategies cannot achieve such a constant-gap approximation for arbitrary networks and propose a new quantizemap-and-forward scheme that does. We also give several extensions of the approximation framework including robustness results (through compound channels), half-duplex constraints and ergodic channel variations.