Efficient operation of coded packet networks

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2006.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Includes bibliographical references (p. [109]-122).A fundamental problem faced in the design of almost all packet networks is that of efficient operation -- of reliably communicating given messages among nodes at minimum cost in resource usage. We present a solution to the efficient operation problem for coded packet networks, i.e., packet networks where the contents of outgoing packets are arbitrary, causal functions of the contents of received packets. Such networks are in contrast to conventional, routed packet networks, where outgoing packets are restricted to being copies of received packets and where reliability is provided by the use of retransmissions. This thesis introduces four considerations to coded packet networks: 1. efficiency, 2. the lack of synchronization in packet networks, 3. the possibility of broadcast links, and 4. packet loss. We take these considerations and give a prescription for operation that is novel and general, yet simple, useful, and extensible. We separate the efficient operation problem into two smaller problems, which we call network coding -- the problem of deciding what coding operation each node should perform given the rates at which packets are injected on each link -- and subgraph selection -- the problem of deciding those rates.(cont.) Our main contribution for the network coding problem is to give a scheme that achieves the maximum rate of a multicast connection under the given injection rates. As a consequence, the separation of network coding and subgraph selection results in no loss of optimality provided that we are constrained to only coding packets within a single connection. Our main contribution for the subgraph selection problem is to give distributed algorithms that optimally solve the single-connection problem under certain assumptions. Since the scheme we propose for network coding can easily be implemented in a distributed manner, we obtain, by combining the solutions for each of the smaller problems, a distributed approach to the efficient operation problem. We assess the performance of our solution for three problems: minimum-transmission wireless unicast, minimum-weight wireline multicast, and minimum-energy wireless multicast. We find that our solution has the potential to offer significant efficiency improvements over existing techniques in routed packet networks, particularly for multi-hop wireless networks.by Desmond S. Lun.Ph.D

ARQ for Network Coding

A new coding and queue management algorithm is proposed for communication networks that employ linear network coding. The algorithm has the feature that the encoding process is truly online, as opposed to a block-by-block approach. The setup assumes a packet erasure broadcast channel with stochastic arrivals and full feedback, but the proposed scheme is potentially applicable to more general lossy networks with link-by-link feedback. The algorithm guarantees that the physical queue size at the sender tracks the backlog in degrees of freedom (also called the virtual queue size). The new notion of a node "seeing" a packet is introduced. In terms of this idea, our algorithm may be viewed as a natural extension of ARQ schemes to coded networks. Our approach, known as the drop-when-seen algorithm, is compared with a baseline queuing approach called drop-when-decoded. It is shown that the expected queue size for our approach is $O(\frac1{1-\rho})$ as opposed to $\Omega(\frac1{(1-\rho)^2})$ for the baseline approach, where $\rho$ is the load factor.Comment: Submitted to the 2008 IEEE International Symposium on Information Theory (ISIT 2008

Optimality of Network Coding in Packet Networks

We resolve the question of optimality for a well-studied packetized implementation of random linear network coding, called PNC. In PNC, in contrast to the classical memoryless setting, nodes store received information in memory to later produce coded packets that reflect this information. PNC is known to achieve order optimal stopping times for the many-to-all multicast problem in many settings. We give a reduction that captures exactly how PNC and other network coding protocols use the memory of the nodes. More precisely, we show that any such protocol implementation induces a transformation which maps an execution of the protocol to an instance of the classical memoryless setting. This allows us to prove that, for any (non-adaptive dynamic) network, PNC converges with high probability in optimal time. In other words, it stops at exactly the first time in which in hindsight it was possible to route information from the sources to each receiver individually. Our technique also applies to variants of PNC, in which each node uses only a finite buffer. We show that, even in this setting, PNC stops exactly within the time in which in hindsight it was possible to route packets given the memory constraint, i.e., that the memory used at each node never exceeds its buffer size. This shows that PNC, even without any feedback or explicit memory management, allows to keep minimal buffer sizes while maintaining its capacity achieving performance

Network Coding Meets TCP: Theory and Implementation

The theory of network coding promises significant benefits in network performance, especially in lossy networks and in multicast and multipath scenarios. To realize these benefits in practice, we need to understand how coding across packets interacts with the acknowledgment (ACK)-based flow control mechanism that forms a central part of today's Internet protocols such as transmission control protocol (TCP). Current approaches such as rateless codes and batch-based coding are not compatible with TCP's retransmission and sliding-window mechanisms. In this paper, we propose a new mechanism called TCP/NC that incorporates network coding into TCP with only minor changes to the protocol stack, thereby allowing incremental deployment. In our scheme, the source transmits random linear combinations of packets currently in the congestion window. At the heart of our scheme is a new interpretation of ACKs-the sink acknowledges every degree of freedom (i.e., a linear combination that reveals one unit of new information) even if it does not reveal an original packet immediately. Thus, our new TCP ACK rule takes into account the network coding operations in the lower layer and enables a TCP-compatible sliding-window approach to network coding. Coding essentially masks losses from the congestion control algorithm and allows TCP/NC to react smoothly to losses, resulting in a novel and effective approach for congestion control over lossy networks such as wireless networks. An important feature of our solution is that it allows intermediate nodes to perform re-encoding of packets, which is known to provide significant throughput gains in lossy networks and multicast scenarios. Simulations show that our scheme, with or without re-encoding inside the network, achieves much higher throughput compared to TCP over lossy wireless links. We present a real-world implementation of this protocol that addresses the practical aspects of incorporating network coding and decoding with TCP's wind ow management mechanism. We work with TCP-Reno, which is a widespread and practical variant of TCP. Our implementation significantly advances the goal of designing a deployable, general, TCP-compatible protocol that provides the benefits of network coding.National Science Foundation (U.S.) (Grant CNS-0627021)National Science Foundation (U.S.) (Grant CNS-0721491)National Science Foundation (U.S.) (Grant CCF-0915922)United States. Defense Advanced Research Projects Agency (Subcontract 18870740-37362-C)United States. Defense Advanced Research Projects Agency (Subcontract 060786)United States. Defense Advanced Research Projects Agency (Subcontract 069145)United States. Defense Advanced Research Projects Agency (Contract N66001-06-C-2020)Space and Naval Warfare Systems Center San Diego (U.S.) (Contract N66001- 08-C-2013

Congestion Control and Routing over Challenged Networks

This dissertation is a study on the design and analysis of novel, optimal routing and rate control algorithms in wireless, mobile communication networks. Congestion control and routing algorithms upto now have been designed and optimized for wired or wireless mesh networks. In those networks, optimal algorithms (optimal in the sense that either the throughput is maximized or delay is minimized, or the network operation cost is minimized) can be engineered based on the classic time scale decomposition assumption that the dynamics of the network are either fast enough so that these algorithms essentially see the average or slow enough that any changes can be tracked to allow the algorithms to adapt over time. However, as technological advancements enable integration of ever more mobile nodes into communication networks, any rate control or routing algorithms based, for example, on averaging out the capacity of the wireless mobile link or tracking the instantaneous capacity will perform poorly. The common element in our solution to engineering efficient routing and rate control algorithms for mobile wireless networks is to make the wireless mobile links seem as if they are wired or wireless links to all but few nodes that directly see the mobile links (either the mobiles or nodes that can transmit to or receive from the mobiles) through an appropriate use of queuing structures at these selected nodes. This approach allows us to design end-to-end rate control or routing algorithms for wireless mobile networks so that neither averaging nor instantaneous tracking is necessary

Energy aware network coding in wireless networks

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2012.Cataloged from PDF version of thesis.Includes bibliographical references (p. 97-104).Energy is one of the most important considerations in designing reliable low-power wireless communication networks. We focus on the problem of energy aware network coding. In particular, we investigate practical energy efficient network code design for wireless body area networks (WBAN). We first consider converge-cast in a star-shaped topology, in which a central base station (BS), or hub, manages and communicates directly with a set of nodes. We then consider a wireless-relay channel, in which a relay node assists in the transmission of data from a source to a destination. This wireless relay channel can be seen as a simplified extended star network, where nodes have relay capabilities. The objective is to investigate the use of network coding in these scenarios, with the goal of achieving reliability under low-energy and lower-power constraints. More specifically, in a star network, we propose a simple network layer protocol, study the mean energy to complete uploads of given packets from the nodes to the BS using a Markov chain model, and show through numerical examples that when reception energy is taken into account, the incorporation of network coding offers reductions in energy use. The amount of achievable gains depends on the number of nodes in the network, the degree of asymmetry in channel conditions experienced by different nodes, and the relative difference between transmitting and receiving power at the nodes. We also demonstrate the compatibility of the proposed scheme with the IEEE 802.15.6 WBAN standard by describing ways of incorporating network coding into systems compliant to the standard. For a wireless relay channel, we explore the strategic use of network coding according to both throughput and energy metrics. In the relay channel, a single source communicates to a single sink through the aid of a half-duplex relay. The fluid flow model is used to describe the case where both the source and the relay are coding, and Markov chain models are proposed to describe packet evolution if only the source or only the relay is coding. Although we do not attempt to explicitly categorize the optimal network coding strategies in the relay channel under different system parameters, we provide a framework for deciding whether and where to code, taking into account of throughput maximization and energy depletion constraints.by Xiaomeng Shi.Ph.D

On the role of feedback in network coding

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2009.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Cataloged from student submitted PDF version of thesis.Includes bibliographical references (p. 143-149).Network coding has emerged as a new approach to operating communication networks, with a promise of improved efficiency in the form of higher throughput, especially in lossy conditions. In order to realize this promise in practice, the interfacing of network coding with existing network protocols must be understood well. Most current protocols make use of feedback in the form of acknowledgments (ACKs) for reliability, rate control and/or delay control. In this work, we propose a way to incorporate network coding within such a feedback-based framework, and study the various benefits of using feedback in a network coded system. More specifically, we propose a mechanism that provides a clean interface between network coding and TCP with only minor changes to the protocol stack, thereby allowing incremental deployment. In our scheme, the source transmits random linear combinations of packets currently in the TCP congestion window. At the heart of our scheme is a new interpretation of ACKs - the receiver acknowledges every degree of freedom (i.e., a linear combination that reveals one unit of new information) even if it does not reveal an original packet immediately. Such ACKs enable a TCP-compatible sliding-window implementation of network coding. Thus, with feedback, network coding can be performed in a completely online manner, without the need for batches or generations. Our scheme has the nice feature that packet losses on the link can be essentially masked from the congestion control algorithm by adding enough redundancy in the encoding process.(cont.) This results in a novel and effective approach for congestion control over networks involving lossy links such as wireless links. Our scheme also allows intermediate nodes to perform re-encoding of the data packets. This in turn leads to a natural way of running TCP flows over networks that use multipath opportunistic routing along with network coding. We use the new type of ACKs to develop queue management algorithms for coded networks, which allow the queue size at nodes to track the true backlog in information with respect to the destination. We also propose feedback-based adaptive coding techniques that are aimed at reducing the decoding delay at the receivers. Different notions of decoding delay are considered, including an order-sensitive notion which assumes that packets are useful only when delivered in order. We study the asymptotic behavior of the expected queue size and delay, in the limit of heavy traffic.by Jay Kumar Sundararajan.Ph.D

Probabilistic methods for distributed information dissemination

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2013.Cataloged from PDF version of thesis.Includes bibliographical references (p. 457-484).The ever-increasing growth of modern networks comes with a paradigm shift in network operation. Networks can no longer be abstracted as deterministic, centrally controlled systems with static topologies but need to be understood as highly distributed, dynamic systems with inherent unreliabilities. This makes many communication, coordination and computation tasks challenging and in many scenarios communication becomes a crucial bottleneck. In this thesis, we develop new algorithms and techniques to address these challenges. In particular we concentrate on broadcast and information dissemination tasks and introduce novel ideas on how randomization can lead to powerful, simple and practical communication primitives suitable for these modern networks. In this endeavor we combine and further develop tools from different disciplines trying to simultaneously addresses the distributed, information theoretic and algorithmic aspects of network communication. The two main probabilistic techniques developed to disseminate information in a network are gossip and random linear network coding. Gossip is an alternative to classical flooding approaches: Instead of nodes repeatedly forwarding information to all their neighbors, gossiping nodes forward information only to a small number of (random) neighbors. We show that, when done right, gossip disperses information almost as quickly as flooding, albeit with a drastically reduced communication overhead. Random linear network coding (RLNC) applies when a large amount of information or many messages are to be disseminated. Instead of routing messages through intermediate nodes, that is, following a classical store-and-forward approach, RLNC mixes messages together by forwarding random linear combinations of messages. The simplicity and topology-obliviousness of this approach makes RLNC particularly interesting for the distributed settings considered in this thesis. Unfortunately the performance of RLNC was not well understood even for the simplest such settings. We introduce a simple yet powerful analysis technique that allows us to prove optimal performance guarantees for all settings considered in the literature and many more that were not analyzable so far. Specifically, we give many new results for RLNC gossip algorithms, RLNC algorithms for dynamic networks, and RLNC with correlated data. We also provide a novel highly efficient distributed implementation of RLNC that achieves these performance guarantees while buffering only a minimal amount of information at intermediate nodes. We then apply our techniques to improve communication primitives in multi-hop radio networks. While radio networks inherently support broadcast communications, e.g., from one node to all surrounding nodes, interference of simultaneous transmissions makes multihop broadcast communication an interesting challenge. We show that, again, randomization holds the key for obtaining simple, efficient and distributed information dissemination protocols. In particular, using random back-off strategies to coordinate access to the shared medium leads to optimal gossip-like communications and applying RLNC achieves the first throughput-optimal multi-message communication primitives. Lastly we apply our probabilistic approach for analyzing simple, distributed propagation protocols in a broader context by studying algorithms for the Lovász Local Lemma. These algorithms find solutions to certain local constraint satisfaction problems by randomly fixing and propagating violations locally. Our two main results show that, firstly, there are also efficient deterministic propagation strategies achieving the same and, secondly, using the random fixing strategy has the advantage of producing not just an arbitrary solution but an approximately uniformly random one. Both results lead to simple, constructions for a many locally consistent structures of interest that were not known to be efficiently constructable before.by Bernhard Haeupler.Ph.D