Browsing by Subject "Index Coding"
Now showing 1 - 2 of 2
Results Per Page
Sort Options
Item Network and Index Coding with Application to Robust and Secure Communications(2011-02-22) El Rouayheb, Salim Y.Since its introduction in the year 2000 by Ahlswede et al., the network coding paradigm has revolutionized the way we understand information flows in networks. Traditionally, information transmitted in a communication network was treated as a commodity in a transportation network, much like cars on highways or fluids in pipes. This approach, however, fails to capture the very nature of information, which in contrast to material goods, can be coded and decoded. The network coding techniques take full advantage of the inherent properties of information, and allow the nodes in a network, not only to store and forward, but also to "mix", i.e., encode, their received data. This approach was shown to result in a substantial throughput gain over the traditional routing and tree packing techniques. In this dissertation, we study applications of network coding for guarantying reliable and secure information transmission in networks with compromised edges. First, we investigate the construction of robust network codes for achieving network resilience against link failures. We focus on the practical important case of unicast networks with non-uniform edge capacities where a single link can fail at a time. We demonstrate that these networks exhibit unique structural properties when they are minimal, i.e., when they do not contain redundant edges. Based on this structure, we prove that robust linear network codes exist for these networks over GF(2), and devise an efficient algorithm to construct them. Second, we consider the problem of securing a multicast network against an eavesdropper that can intercept the packets on a limited number of network links. We recast this problem as a network generalization of the classical wiretap channel of Type II introduced by Ozarow and Wyner in 1984. In particular, we demonstrate that perfect secrecy can be achieved by using the Ozarow-Wyner scheme of coset coding at the source, on top of the implemented network code. Consequently, we transparently recover important results available in the literature on secure network coding. We also derive new bounds on the required secure code alphabet size and an algorithm for code construction. In the last part of this dissertation, we study the connection between index coding, network coding, and matroid linear representation. We devise a reduction from the index coding problem to the network coding problem, implying that in the linear case these two problems are equivalent. We also present a second reduction from the matroid linear representability problem to index coding, and therefore, to network coding. The latter reduction establishes a strong connection between matroid theory and network coding theory. These two reductions are then used to construct special instances of the index coding problem where vector linear codes outperform scalar linear ones, and where non-linear encoding is needed to achieve the optimal number of transmission. Thereby, we provide a counterexample to a related conjecture in the literature and demonstrate the benefits of vector linear codes.Item Network Coding in Distributed, Dynamic, and Wireless Environments: Algorithms and Applications(2012-02-14) Chaudhry, MohammadThe network coding is a new paradigm that has been shown to improve throughput, fault tolerance, and other quality of service parameters in communication networks. The basic idea of the network coding techniques is to relish the "mixing" nature of the information flows, i.e., many algebraic operations (e.g., addition, subtraction etc.) can be performed over the data packets. Whereas traditionally information flows are treated as physical commodities (e.g., cars) over which algebraic operations can not be performed. In this dissertation we answer some of the important open questions related to the network coding. Our work can be divided into four major parts. Firstly, we focus on network code design for the dynamic networks, i.e., the networks with frequently changing topologies and frequently changing sets of users. Examples of such dynamic networks are content distribution networks, peer-to-peer networks, and mobile wireless networks. A change in the network might result in infeasibility of the previously assigned feasible network code, i.e., all the users might not be able to receive their demands. The central problem in the design of a feasible network code is to assign local encoding coefficients for each pair of links in a way that allows every user to decode the required packets. We analyze the problem of maintaining the feasibility of a network code, and provide bounds on the number of modifications required under dynamic settings. We also present distributed algorithms for the network code design, and propose a new path-based assignment of encoding coefficients to construct a feasible network code. Secondly, we investigate the network coding problems in wireless networks. It has been shown that network coding techniques can significantly increase the overall throughput of wireless networks by taking advantage of their broadcast nature. In wireless networks each packet transmitted by a device is broadcasted within a certain area and can be overheard by the neighboring devices. When a device needs to transmit packets, it employs the Index Coding that uses the knowledge of what the device's neighbors have heard in order to reduce the number of transmissions. With the Index Coding, each transmitted packet can be a linear combination of the original packets. The Index Coding problem has been proven to be NP-hard, and NP-hard to approximate. We propose an efficient exact, and several heuristic solutions for the Index Coding problem. Noting that the Index Coding problem is NP-hard to approximate, we look at it from a novel perspective and define the Complementary Index Coding problem, where the objective is to maximize the number of transmissions that are saved by employing coding compared to the solution that does not involve coding. We prove that the Complementary Index Coding problem can be approximated in several cases of practical importance. We investigate both the multiple unicast and multiple multicast scenarios for the Complementary Index Coding problem for computational complexity, and provide polynomial time approximation algorithms. Thirdly, we consider the problem of accessing large data files stored at multiple locations across a content distribution, peer-to-peer, or massive storage network. Parts of the data can be stored in either original form, or encoded form at multiple network locations. Clients access the parts of the data through simultaneous downloads from several servers across the network. For each link used client has to pay some cost. A client might not be able to access a subset of servers simultaneously due to network restrictions e.g., congestion etc. Furthermore, a subset of the servers might contain correlated data, and accessing such a subset might not increase amount of information at the client. We present a novel efficient polynomial-time solution for this problem that leverages the matroid theory. Fourthly, we explore applications of the network coding for congestion mitigation and over flow avoidance in the global routing stage of Very Large Scale Integration (VLSI) physical design. Smaller and smarter devices have resulted in a significant increase in the density of on-chip components, which has given rise to congestion and over flow as critical issues in on-chip networks. We present novel techniques and algorithms for reducing congestion and minimizing over flows.