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., 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. Index Terms—Algebraic coding, network information theory, network robustness. I.

We propose a new scheme for content distribution of large files that is based on network coding. With network coding, each node of the distribution network is able to generate and transmit encoded blocks of information. The randomization introduced by the coding process eases the scheduling of block propagation, and, thus, makes the distribution more efficient. This is particularly important in large unstructured overlay networks, where the nodes need to make decisions based on local information only. We compare network coding to other schemes that transmit unencoded information (i.e. blocks of the original file) and, also, to schemes in which only the source is allowed to generate and transmit encoded packets. We study the performance of network coding in heterogeneous networks with dynamic node arrival and departure patterns, clustered topologies, and when incentive mechanisms to discourage free-riding are in place. We demonstrate through simulations of scenarios of practical interest that the expected file download time improves by more than 20-30 % with network coding compared to coding at the server only and, by more than 2-3 times compared to sending unencoded information. Moreover, we show that network coding improves the robustness of the system and is able to smoothly handle extreme situations where the server and nodes departure the system.

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.

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.

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Abstract — We study communication networks of arbitrary size and topology and communicating over a general vector discrete memoryless channel. We propose an information-theoretic constructive scheme for obtaining an achievable rate region in such networks. Many well-known capacity-defining achievable rate regions can be derived as special cases of the proposed scheme. A few such examples are the physically degraded and reverselydegraded relay channels, the Gaussian multiple-access channel, and the Gaussian broadcast channel. The proposed scheme also leads to inner bounds for the multicast and allcast capacities. Applying the proposed scheme to a specific wireless network   of nodes located in a region of unit area, we show that a transport capacity of ¡£ ¢ bit-meters/sec is feasible in a certain family of networks, as compared to the best possible transport capacity ¡£¢§ ¦   ¨ ¤ of bit-meters/sec in [16] where the receiver capabilities were limited. Even though the improvement is shown for a specific class of networks, a clear implication is that designing and employing more sophisticated multi-user coding schemes can provide sizable gains in at least some large wireless networks. Index Terms — Discrete memoryless channels, Gaussian channels, multiuser communications, network information theory,

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.

Abstract — In recent years, BitTorrent has emerged as a very scalable peer-to-peer file distribution mechanism. While early measurement and analytical studies have verified BitTorrent’s performance, they have also raised questions about various metrics (upload utilization, fairness, etc.), particularly in settings other than those measured. In this paper, we present a simulationbased study of BitTorrent. Our goal is to deconstruct the system and evaluate the impact of its core mechanisms, both individually and in combination, on overall system performance under a variety of workloads. Our evaluation focuses on several important metrics, including peer link utilization, file download time, and fairness amongst peers in terms of volume of content served. Our results confirm that BitTorrent performs near-optimally in terms of uplink bandwidth utilization, and download time except under certain extreme conditions. We also show that low bandwidth peers can download more than they upload to the network when high bandwidth peers are present. We find that the rate-based tit-for-tat policy is not effective in preventing unfairness. We show how simple changes to the tracker and a stricter, block-based tit-for-tat policy, greatly improves fairness. I.

The famous max-flow min-cut theorem states that a source node s can send information through a network (V; E) to a sink node t at a data rate determined by the min-cut separating s and t. Recently it has been shown that this rate can also be achieved for multicasting to several sinks provided that the intermediate nodes are allowed to reencode the information they receive. In contrast, we present graphs where without coding the rate must be a factor jV j) smaller. However, so far no fast algorithms for constructing appropriate coding schemes were known. Our main result are polynomial time algorithms for constructing coding schemes for multicasting at the maximal data rate.

Abstract—It is known that every solvable multicast network has a scalar linear solution over a sufficiently large finite-field alphabet. It is also known that this result does not generalize to arbitrary networks. There are several examples in the literature of solvable networks with no scalar linear solution over any finite field. However, each example has a linear solution for some vector dimension greater than one. It has been conjectured that every solvable network has a linear solution over some finite-field alphabet and some vector dimension. We provide a counterexample to this conjecture. We also show that if a network has no linear solution over any finite field, then it has no linear solution over any finite commutative ring with identity. Our counterexample network has no linear solution even in the more general algebraic context of modules, which includes as special cases all finite rings and Abelian groups. Furthermore, we show that the network coding capacity of this network is strictly greater than the maximum linear coding capacity over any finite field (exactly 10 % greater), so the network is not even asymptotically linearly solvable. It follows that, even for more general versions of linearity such as convolutional coding, filter-bank coding, or linear time sharing, the network has no linear solution. Index Terms—Asymptotics, flows, linear coding, network information theory, routing. I.