We present a capacity-approaching coding scheme for unicast or multicast over lossy packet networks. In the scheme, all nodes perform coding, but do not wait for a full block of packets to be received before sending out coded packets. Rather, whenever they have a transmission opportunity, they form coded packets with random linear combinations of previously received packets. All coding and decoding operations in the scheme have polynomial complexity. Our analysis of the scheme shows that it is not only capacity-approaching, but that the propagation of packets carrying “innovative ” information follows that of a queueing network where every node acts as a stable M/M/1 queue. We consider networks with both lossy point-to-point and broadcast links, allowing us to model both wireline and wireless packet networks. 1

Abstract — We consider the problem of storing a large file or multiple large files in a distributed manner over a network. In the framework we consider, there are multiple storage locations, each of which only have very limited storage space for each file. Each storage location chooses a part (or a coded version of the parts) of the file without the knowledge of what is stored in the other locations. We want a file-downloader to connect to as few storage locations as possible and retrieve the entire file. We compare the performance of three strategies: uncoded storage, traditional erasure coding based storage, random linear coding based storage motivated by network coding. We demonstrate that, in principle, a traditional erasure coding based storage (eg: Reed-Solomon Codes) strategy can almost do as well as one can ask for with appropriate choice of parameters. However, the cost is a large amount of additional storage space required at the centralized server before distribution among multiple locations. The random linear coding based strategy performs as well without suffering from any such disadvantage. Further, with a probability close to one, the minimum number of storage location a downloader needs to connect to (for reconstructing the entire file), can be very close to the case where there is complete coordination between the storage locations and the downloader. We also argue that an uncoded strategy performs poorly. I.

We show that network coding allows to realize energy savings in a wireless ad-hoc network, when each node of the network is a source that wants to transmit information to all other nodes. Energy efficiency directly affects battery life and thus is a critical design parameter for wireless networks. We propose an implementable method for performing network coding in such a setting. We analyze theoretical cases in detail, and use the insights gained to propose a practical, fully distributed method for realistic wireless ad-hoc scenarios. We address practical issues such as setting the forwarding factor, managing generations, and impact of transmission range. We use theoretical analysis and packet level simulation.

Abstract — This paper investigates the dissemination of multiple pieces of information in large networks where users contact each other in a random uncoordinated manner, and users upload one piece per unit time. The underlying motivation is the design and analysis of piece selection protocols for peer-to-peer networks which disseminate files by dividing them into pieces. We first investigate one-sided protocols, where piece selection is based on the states of either the transmitter or the receiver. We show that any such protocol relying only on pushes, or alternatively only on pulls, will be inefficient in disseminating all pieces to all users. We propose a hybrid one-sided piece selection protocol – INTERLEAVE – and show that by using both pushes and pulls it disseminates k pieces from a single source to n users in 10(k + log n) time, while obeying the constraint that each user can upload at most one piece in one unit of time. An optimal, unrealistic centralized protocol would take k+log 2 n time in this setting. Moreover, efficient dissemination is also possible if the source implements forward erasure coding, and users push the latest-released coded pieces (but do not pull). We also investigate two-sided protocols where piece selection is based on the states of both the trasmitter and the receiver. We show that it is possible to disseminate n pieces to n users in n + O(log n) time, starting from an initial state where each user has a unique piece. I.

Abstract — This paper analyzes the gains in delay performance resulting from network coding. We consider a model of file transmission to multiple receivers from a single base station. Using this model, we show that gains in delay performance from network coding with or without channel side information can be substantial compared to conventional scheduling methods for downlink transmission. I.

Abstract — Energy efficiency, i.e., the amount of battery energy consumed to transmit bits across a wireless link, is a critical design parameter for wireless ad-hoc networks. We examine the problem of broadcasting information to all nodes in an ad-hoc network, when a large percentage of the nodes act as sources. We theoretically quantify the energy savings that network coding can offer for the cases of two regular topologies. We then propose low-complexity distributed algorithms, and demonstrate through simulation that for random networks, network coding can in fact offer significant benefits in terms of energy consumption. I.

In this paper, we investigate the benefits of using a form of network coding known as Random Linear Coding (RLC) for unicast communications in a mobile Disruption Tolerant Network (DTN) under epidemic routing. Under RLC, DTN nodes store and then forward random linear combinations of packets as they encounter other DTN nodes. We first consider RLC applied to a single block of packets where (a) all packets have the same source and destination, (b) the packets have different sources but a common destination and (c) the packets each have a different source/destination pair; we also consider the case where blocks of packets arrive according to a Poisson bulk arrival process. Our performance metric of interest is the delay until the last packet in a block is delivered. We show that for the single block case, when bandwidth is constrained, applying RLC over packets destined to the same node achieves (with high probability) the minimum delay to deliver the block of data. We find through simulation that the benefit over non-network-coded packet forwarding increases further when buffer space within DTN nodes is limited. For the case of multiple blocks, our simulations show that RLC offers only slight improvement over the non-coded scenario when only bandwidth is constrained, but more significant benefits when both bandwidth and buffers are constrained. We remark that when the network is relatively loaded, RLC achieves improvements over non-coding scheme only if the spreading of the information is appropriately controlled. 1

We consider the problem of broadcasting in an adhoc wireless network, where all nodes of the network are sources that want to transmit information to all other nodes. Our figure of merit is energy efficiency, a critical design parameter for wireless networks since it directly affects battery life and thus network lifetime. We prove that applying ideas from network coding allows to realize significant benefits in terms of energy efficiency for the problem of broadcasting, and propose very simple algorithms that allow to realize these benefits in practice. In particular, our theoretical analysis shows that network coding improves performance by a constant factor in fixed networks. We calculate this factor exactly for some canonical configurations. We then show that in networks where the topology dynamically changes, for example due to mobility, and where operations are restricted to simple distributed algorithms, network coding can offer improvements of a factor of log n, where n is the number of nodes in the network. We use the insights gained from the theoretical analysis to propose low-complexity distributed algorithms for realistic wireless ad-hoc scenarios, discuss a number of practical considerations, and evaluate our algorithms through packet level simulation.

Abstract — We consider a finite-field model for the wireless broadcast and additive interference network (WBAIN), both in the presence and absence of fading. We show that the singlesource unicast capacity (with extension to multicast) of a WBAIN with or without fading can be upper bounded by the capacity of an equivalent broadcast erasure network. We further present a coding strategy for WBAINs with i.i.d. and uniform fading based on random linear coding at each node that achieves a rate differing from the upper bound by no more than O(1/q), where q is the field size. Using these results, we show that channel fading in conjunction with network coding can lead to large gains in the unicast (multicast) capacity as compared to no fading. I.

Live peer-to-peer (P2P) streaming has recently received much research attention, with successful commercial systems showing its viability in the Internet. Nevertheless, existing analytical studies of P2P streaming systems have failed to mathematically investigate and understand their critical properties, especially with a large scale and under extreme dynamics such as a flash crowd scenario. Even more importantly, there exists no prior analytical work that focuses on an entirely new way of designing streaming protocols, with the help of network coding. In this paper, we seek to show an in-depth analytical understanding of fundamental properties of P2P streaming systems, with a particular spotlight on the benefits of network coding. We show that, if network coding is used according to certain design principles, provably good performance can be guaranteed, with respect to high playback qualities, short initial buffering delays, resilience to peer dynamics, as well as minimal bandwidth costs on dedicated streaming servers. Our results are obtained with mathematical rigor, but without sacrificing realistic assumptions of system scale, peer dynamics, and upload capacities. For further insights, streaming systems using network coding are compared with traditional pull-based streaming in large-scale simulations, with a focus on fundamentals, rather than protocol details. The scale of our simulations throughout this paper exceeds 200, 000 peers at times, which is in sharp contrast with existing empirical studies, typically with a few hundred peers involved.