Optimal Deterministic Polynomial-Time Data Exchange for Omniscience

We study the problem of constructing a deterministic polynomial time algorithm that achieves omniscience, in a rate-optimal manner, among a set of users that are interested in a common file but each has only partial knowledge about it as side-information. Assuming that the collective information among all the users is sufficient to allow the reconstruction of the entire file, the goal is to minimize the (possibly weighted) amount of bits that these users need to exchange over a noiseless public channel in order for all of them to learn the entire file. Using established connections to the multi-terminal secrecy problem, our algorithm also implies a polynomial-time method for constructing a maximum size secret shared key in the presence of an eavesdropper. We consider the following types of side-information settings: (i) side information in the form of uncoded fragments/packets of the file, where the users' side-information consists of subsets of the file; (ii) side information in the form of linearly correlated packets, where the users have access to linear combinations of the file packets; and (iii) the general setting where the the users' side-information has an arbitrary (i.i.d.) correlation structure. Building on results from combinatorial optimization, we provide a polynomial-time algorithm (in the number of users) that, first finds the optimal rate allocations among these users, then determines an explicit transmission scheme (i.e., a description of which user should transmit what information) for cases (i) and (ii)

Network coding meets multimedia: a review

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 mediaspecific 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 networkin

Anonymous Networking amidst Eavesdroppers

The problem of security against timing based traffic analysis in wireless networks is considered in this work. An analytical measure of anonymity in eavesdropped networks is proposed using the information theoretic concept of equivocation. For a physical layer with orthogonal transmitter directed signaling, scheduling and relaying techniques are designed to maximize achievable network performance for any given level of anonymity. The network performance is measured by the achievable relay rates from the sources to destinations under latency and medium access constraints. In particular, analytical results are presented for two scenarios: For a two-hop network with maximum anonymity, achievable rate regions for a general m x 1 relay are characterized when nodes generate independent Poisson transmission schedules. The rate regions are presented for both strict and average delay constraints on traffic flow through the relay. For a multihop network with an arbitrary anonymity requirement, the problem of maximizing the sum-rate of flows (network throughput) is considered. A selective independent scheduling strategy is designed for this purpose, and using the analytical results for the two-hop network, the achievable throughput is characterized as a function of the anonymity level. The throughput-anonymity relation for the proposed strategy is shown to be equivalent to an information theoretic rate-distortion function

On Coding for Reliable Communication over Packet Networks

We present a capacity-achieving coding scheme for unicast or multicast over lossy packet networks. In the scheme, intermediate nodes perform additional coding yet do not decode nor even wait for a block of packets before sending out coded packets. Rather, whenever they have a transmission opportunity, they send out coded packets formed from random linear combinations of previously received packets. All coding and decoding operations have polynomial complexity. We show that the scheme is capacity-achieving as long as packets received on a link arrive according to a process that has an average rate. Thus, packet losses on a link may exhibit correlation in time or with losses on other links. In the special case of Poisson traffic with i.i.d. losses, we give error exponents that quantify the rate of decay of the probability of error with coding delay. Our analysis of the scheme shows that it is not only capacity-achieving, but that the propagation of packets carrying "innovative" information follows the propagation of jobs through a queueing network, and therefore fluid flow models yield good approximations. We consider networks with both lossy point-to-point and broadcast links, allowing us to model both wireline and wireless packet networks.Comment: 33 pages, 6 figures; revised appendi

Achieving Quality of Service Guarantees for Delay Sensitive Applications in Wireless Networks

In the past few years, we have witnessed the continuous growth in popularity of delay-sensitive applications. Applications like live video streaming, multimedia conferencing, VoIP and online gaming account for a major part of Internet traffic these days. It is also predicted that this trend will continue in the coming years. This emphasizes the significance of developing efficient scheduling algorithms in communication networks with guaranteed low delay performance. In our work, we try to address the delay issue in some major instances of wireless communication networks. First, we study a wireless content distribution network (CDN), in which the requests for the content may have service deadlines. Our wireless CDN consists of a media vault that hosts all the content in the system and a number of local servers (base stations), each having a cache for temporarily storing a subset of the content. There are two major questions associated with this framework: (i) content caching: which content should be loaded in each cache? and (ii) wireless network scheduling: how to appropriately schedule the transmissions from wireless servers? Using ideas from queuing theory, we develop provably optimal algorithms to jointly solve the caching and scheduling problems. Next, we focus on wireless relay networks. It is well accepted that network coding can enhance the performance of these networks by exploiting the broadcast nature of the wireless medium. This improvement is usually evaluated in terms of the number of required transmissions for delivering flow packets to their destinations. In this work, we study the effect of delay on the performance of network coding by characterizing a trade-off between latency and the performance gain achieved by employing network coding. More specifically, we associate a holding cost for delaying packets before delivery and a transmission cost for each broadcast transmission made by the relay node. Using a Markov decision process (MDP) argument, we prove a simple threshold-based policy is optimal in the sense of minimum long-run average cost. Finally, we analyze delay-sensitive applications in wireless peer-to-peer (P2P) networks. We consider a hybrid network which consists of (i) an expensive base station-to-peer (B2P) network with unicast transmissions, and (ii) a free broadcast P2P network. In such a framework, we study two popular applications: (a) a content distribution application with service deadlines, and (b) a multimedia live streaming application. In both problems, we utilize random linear network coding over finite fields to simplify the coordination of the transmissions. For these applications, we provide efficient algorithms to schedule the transmissions such that some quality of service (QoS) requirements are satisfied with the minimum cost of B2P usage. The algorithms are proven to be throughput optimal for sufficiently large field sizes and perform reasonably well for finite fields