There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

We present a distributed random linear network coding approach for transmission and compression of information in general multisource multicast networks. Network nodes independently and randomly select linear mappings from inputs onto output links over some field. We show that this achieves capacity with probability exponentially approaching 1 with the code length. We also demonstrate that random linear coding performs compression when necessary in a network, generalizing error exponents for linear Slepian-Wolf coding in a natural way. Benefits of this approach are decentralized operation and robustness to network changes or link failures. We show that this approach can take advantage of redundant network capacity for improved success probability and robustness. We illustrate some potential advantages of random linear network coding over routing in two examples of practical scenarios: distributed network operation and networks with dynamically varying connections. Our derivation of these results also yields a new bound on required field size for centralized network coding on general multicast networks

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A Random Linear Network Coding Approach to Multicast

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.

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.

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Trading structure for randomness in wireless opportunistic routing

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 block forwarding 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 leave the system.

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Network coding for large scale content distribution

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.

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How Practical is Network Coding

In information theory, it has been shown that network coding can effectively improve the throughput of multicast communication sessions in directed acyclic graphs. More practically, random network coding is also instrumental towards improving the downloading performance in BitTorrent-like peer-to-peer content distribution sessions. Live peer-to-peer streaming, however, poses unique challenges to the use of network coding, due to its strict timing and bandwidth constraints. In this paper, we revisit the complete spectrum in the design space of live peer-to-peer streaming protocols, with a sole objective of taking full advantage of random network coding. We present R2, our new streaming algorithm designed from scratch to incorporate random network coding with a randomized push algorithm. R2 is designed to improve the performance of live streaming in terms of initial buffering delays, resilience to peer dynamics, as well as reduced bandwidth costs on dedicated streaming servers, all of which are beyond the basic requirement of stable streaming playback. On an experimental testbed consisting of dozens of dual-CPU cluster servers, we thoroughly evaluate R2 with an actual implementation, real network traffic, and emulated peer upload capacities, in comparisons with a typical live streaming protocol (both without and with network coding), representing the current state-of-the-art in real-world streaming applications.

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R2: Random Push with Random Network Coding in Live Peer-to-Peer Streaming

In recent literature, network coding has emerged as a promising information theoretic approach to improve the performance of both peer-to-peer and wireless networks. It has been widely accepted and acknowledged that network coding can theoretically improve network throughput of multicast sessions in directed acyclic graphs, achieving their cut-set capacity bounds. Recent studies have also supported the claim that network coding is beneficial for large-scale peer-to-peer content distribution, as it solves the problem of locating the last missing blocks to complete the download. We seek to perform a reality check of using network coding for peer-to-peer live multimedia streaming. We start with the following critical question: How helpful is network coding in peer-to-peer streaming? To address this question, we first implement the decoding process using Gauss-Jordan elimination, such that it can be performed while coded blocks are progressively received. We then implement a realistic testbed, called Lava, with actual network traffic to meticulously evaluate the benefits and tradeoffs involved in using network coding in peer-to-peer streaming. We present the architectural design challenges in implementing network coding for the purpose of streaming, along with a pull-based peer-to-peer live streaming protocol in our comparison studies. Our experimental results show that network coding makes it possible to perform streaming with a finer granularity, which reduces the redundancy of bandwidth usage, improves resilience to network dynamics, and is most instrumental when the bandwidth supply barely meets the streaming demand.

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Lava: A Reality Check of Network Coding in Peer-to-Peer Live Streaming

Existing research work towards the composition of complex federated services has assumed that service requests and deliveries flow through a particular service path or tree. Here, we extend such a service model to a directed acyclic graph, allowing services to be delivered via parallel paths and interleaved with each other. Such an assumption of the service flow model has apparently introduced complexities towards the development of a distributed algorithm to federate existing services, as well as the provisioning of the required quality in the most resource-efficient fashion. To this end, we propose sFlow, a fully distributed algorithm to be executed on all service nodes, such that the federated service flow graph is resource efficient, performs well, and meets the demands of service consumers.

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sFlow: towards resource-efficient and agile service federation in service overlay networks

While every network node only relays messages in a traditional communication system, the recent network coding (NC) paradigm proposes to implement simple in-network processing with packet combinations in the nodes. NC extends the concept of “encoding” a message beyond source coding (for compression) and channel coding (for protection against errors and losses). It has been shown to increase network throughput compared to traditional networks implementation, to reduce delay and to provide robustness to transmission errors and network dynamics. These features are so appealing for multimedia applications that they have spurred a large research effort towards the development of multimedia-specific NC techniques. This paper reviews the recent work in NC for multimedia applications and focuses on the techniques that fill the gap between NC theory and practical applications. It outlines the benefits of NC and presents the open challenges in this area. The paper initially focuses on multimedia-specific aspects of network coding, in particular delay, in-network error control, and media-specific error control. These aspects permit to handle varying network conditions as well as client heterogeneity, which are critical to the design and deployment of multimedia systems. After introducing these general concepts, the paper reviews in detail two applications that lend themselves naturally to NC via the cooperation and broadcast models, namely peer-to-peer multimedia streaming and wireless networking.

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Mea Wang

Papers

How Practical is Network Coding

R2: Random Push with Random Network Coding in Live Peer-to-Peer Streaming

Lava: A Reality Check of Network Coding in Peer-to-Peer Live Streaming

sFlow: towards resource-efficient and agile service federation in service overlay networks

Network Coding Meets Multimedia: A Review