Local network coding on packet erasure channels -- From Shannon capacity to stability region

Network Coding (NC) has emerged as a ubiquitous technique of communication networks and has extensive applications in both practical implementations and theoretical developments. While the Avalanche P2P file system from Microsoft, the MORE routing protocol, and the COPE coding architecture from MIT have implemented the idea of NC and exhibited promising performance improvements, a significant part of the success of NC stems from the continuing theoretic development of NC capacity, e.g., the Shannon capacity results for the single-flow multi-cast network and the packet erasure broadcast channel with feedback. However, characterizing the capacity for the practical wireless multi-flow network setting remains a challenging topic in NC. For example, the difficulties of finding the optimal NC strategy over multiple flows under varying-channel qualities and the rate adaption scenarios hinder any further advancement in this area. Despite the difficulty of characterizing the full capacity for large networks, there are evidences showing that even when using only local operations, NC can still recover substantial NC gain. We believe that a deeper understanding of multi-flow local network coding will play a key role in designing the next-generation high-throughput coding-based wireless network architecture. This thesis consists of three parts. In the first part, we characterize the full Shannon capacity region of the COPE principle when applied to a 2-flow wireless butterfly network with broadcast packet erasure channels. The capacity results allow for random overhearing probabilities, arbitrary scheduling policies, network-wide channel state information (CSI) feedback after each transmission, and potential use of non-linear network codes. We propose a theoretical outer bound and a new class of linear network codes, named the Space-Based Linear Network Coding (SBLNC), that achieves the capacity outer bound. Numerical experiments show that SBLNC provides close-to-optimal throughput even in the scenario with opportunistic routing. In the second part, we further consider the complete network dynamics of stochastic arrivals and queueing and study the corresponding stability region. Based on dynamic packet arrivals, the resulting solution would be one step closer to practical implementation, when compared to the previous block-code-based capacity study. For the 2-flow downlink scenario, we propose the first opportunistic INC + scheduling solution that is provably optimal for time-varying channels, i.e., the corresponding stability region matches the optimal Shannon capacity. Specifically, we first introduce a new binary INC operation, which is distinctly different from the traditional wisdom of XORing two overheard packets. We then develop a queue-length-based scheduling scheme, which, with the help of the new INC operation, can robustly and optimally adapt to time-varying channel quality. We then show that the proposed algorithm can be easily extended for rate adaptation and it again robustly achieves the optimal throughput. In the third part, we propose an 802.11-based MAC layer protocol which incorporates the rate adaption solution developed in the second part. The new MAC protocol realizes the promised intersession network coding gain for two-flow downlink traffic with short decoding delay. Furthermore, we delicately retain the CSMA-CA distributed contention mechanism with only 17 bits new header field changes, and carefully ensure the backward compatibility. In summary, the new solution demonstrates concrete throughput improvement without alternating the too much packet-by-packet traffic behavior. Such a feature is critical in practical implementation since it allows the network coding solution to be transparent to any arbitrary upper layer applications

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

Joint source-channel-network coding in wireless mesh networks with temporal reuse

Technological innovation that empowers tiny low-cost transceivers to operate with a high degree of utilisation efficiency in multihop wireless mesh networks is contributed in this dissertation. Transmission scheduling and joint source-channel-network coding are two of the main aspects that are addressed. This work focuses on integrating recent enhancements such as wireless network coding and temporal reuse into a cross-layer optimisation framework, and to design a joint coding scheme that allows for space-optimal transceiver implementations. Link-assigned transmission schedules with timeslot reuse by multiple links in both the space and time domains are investigated for quasi-stationary multihop wireless mesh networks with both rate and power adaptivity. Specifically, predefined cross-layer optimised schedules with proportionally fair end-to-end flow rates and network coding capability are constructed for networks operating under the physical interference model with single-path minimum hop routing. Extending transmission rights in a link-assigned schedule allows for network coding and temporal reuse, which increases timeslot usage efficiency when a scheduled link experiences packet depletion. The schedules that suffer from packet depletion are characterised and a generic temporal reuse-aware achievable rate region is derived. Extensive computational experiments show improved schedule capacity, quality of service, power efficiency and benefit from opportunistic bidirectional network coding accrued with schedules optimised in the proposed temporal reuse-aware convex capacity region. The application of joint source-channel coding, based on fountain codes, in the broadcast timeslot of wireless two-way network coding is also investigated. A computationally efficient subroutine is contributed to the implementation of the fountain compressor, and an error analysis is done. Motivated to develop a true joint source-channel-network code that compresses, adds robustness against channel noise and network codes two packets on a single bipartite graph and iteratively decodes the intended packet on the same Tanner graph, an adaptation of the fountain compressor is presented. The proposed code is shown to outperform a separated joint source-channel and network code in high source entropy and high channel noise regions, in anticipated support of dense networks that employ intelligent signalling. AFRIKAANS : Tegnologiese innovasie wat klein lae-koste kommunikasie toestelle bemagtig om met ’n hoë mate van benuttings doeltreffendheid te werk word bygedra in hierdie proefskrif. Transmissie-skedulering en gesamentlike bron-kanaal-netwerk kodering is twee van die belangrike aspekte wat aangespreek word. Hierdie werk fokus op die integrasie van onlangse verbeteringe soos draadlose netwerk kodering en temporêre herwinning in ’n tussen-laag optimaliserings raamwerk, en om ’n gesamentlike kodering skema te ontwerp wat voorsiening maak vir spasie-optimale toestel implementerings. Skakel-toegekende transmissie skedules met tydgleuf herwinning deur veelvuldige skakels in beide die ruimte en tyd domeine word ondersoek vir kwasi-stilstaande, veelvuldige-sprong draadlose rooster netwerke met beide transmissie-spoed en krag aanpassings. Om spesifiek te wees, word vooraf bepaalde tussen-laag geoptimiseerde skedules met verhoudings-regverdige punt-tot-punt vloei tempo’s en netwerk kodering vermoë saamgestel vir netwerke wat bedryf word onder die fisiese inmengings-model met enkel-pad minimale sprong roetering. Die uitbreiding van transmissie-regte in ’n skakel-toegekende skedule maak voorsiening vir netwerk kodering en temporêre herwinning, wat tydgleuf gebruiks-doeltreffendheid verhoog wanneer ’n geskeduleerde skakel pakkie-uitputting ervaar. Die skedules wat ly aan pakkie-uitputting word gekenmerk en ’n generiese temporêre herwinnings-bewuste haalbare transmissie-spoed gebied word afgelei. Omvattende berekenings-eksperimente toon verbeterde skedulerings kapasiteit, diensgehalte, krag doeltreffendheid asook verbeterde voordeel wat getrek word uit opportunistiese tweerigting netwerk kodering met die skedules wat geoptimiseer word in die temporêre herwinnings-bewuste konvekse transmissie-spoed gebied. Die toepassing van gesamentlike bron-kanaal kodering, gebaseer op fontein kodes, in die uitsaai-tydgleuf van draadlose tweerigting netwerk kodering word ook ondersoek. ’n Berekenings-effektiewe subroetine word bygedra in die implementering van die fontein kompressor, en ’n foutanalise word gedoen. Gemotiveer om ’n ware gesamentlike bron-kanaal-netwerk kode te ontwikkel, wat robuustheid byvoeg teen kanaal geraas en twee pakkies netwerk kodeer op ’n enkele bipartiete grafiek en die beoogde pakkie iteratief dekodeer op dieselfde Tanner grafiek, word ’n aanpassing van die fontein kompressor aangebied. Dit word getoon dat die voorgestelde kode ’n geskeide gesamentlike bron-kanaal en netwerk kode in hoë bron-entropie en ho¨e kanaal-geraas gebiede oortref in verwagte ondersteuning van digte netwerke wat van intelligente sein-metodes gebruik maak.Dissertation (MEng)--University of Pretoria, 2011.Electrical, Electronic and Computer Engineeringunrestricte

Design and Reliability Performance Evaluation of Network Coding Schemes for Lossy Wireless Networks

This thesis investigates lossy wireless networks, which are wireless communication networks consisting of lossy wireless links, where the packet transmission via a lossy wireless link is successful with a certain value of probability. In particular, this thesis analyses all-to-all broadcast in lossy wireless networks, where every node has a native packet to transmit to all other nodes in the network. A challenge of all-to-all broadcast in lossy wireless networks is the reliability, which is defined as the probability that every node in the network successfully obtains a copy of the native packets of all other nodes. In this thesis, two novel network coding schemes are proposed, which are the neighbour network coding scheme and the random neighbour network coding scheme. In the two proposed network coding schemes, a node may perform a bit-wise exclusive or (XOR) operation to combine the native packet of itself and the native packet of its neighbour, called the coding neighbour, into an XOR coded packet. The reliability of all-to-all broadcast under both the proposed network coding schemes is investigated analytically using Markov chains. It is shown that the reliability of all-to-all broadcast can be improved considerably by employing the proposed network coding schemes, compared with non-coded networks with the same link conditions, i.e. same probabilities of successful packet transmission via wireless channels. Further, the proposed schemes take the link conditions of each node into account to maximise the reliability of a given network. To be more precise, the first scheme proposes the optimal coding neighbour selection method while the second scheme introduces a tuning parameter to control the probability that a node performs network coding at each transmission. The observation that channel condition can have a significant impact on the performance of network coding schemes is expected to be applicable to other network coding schemes for lossy wireless networks

Design and Reliability Performance Evaluation of Network Coding Schemes for Lossy Wireless Networks

This thesis investigates lossy wireless networks, which are wireless communication networks consisting of lossy wireless links, where the packet transmission via a lossy wireless link is successful with a certain value of probability. In particular, this thesis analyses all-to-all broadcast in lossy wireless networks, where every node has a native packet to transmit to all other nodes in the network. A challenge of all-to-all broadcast in lossy wireless networks is the reliability, which is defined as the probability that every node in the network successfully obtains a copy of the native packets of all other nodes. In this thesis, two novel network coding schemes are proposed, which are the neighbour network coding scheme and the random neighbour network coding scheme. In the two proposed network coding schemes, a node may perform a bit-wise exclusive or (XOR) operation to combine the native packet of itself and the native packet of its neighbour, called the coding neighbour, into an XOR coded packet. The reliability of all-to-all broadcast under both the proposed network coding schemes is investigated analytically using Markov chains. It is shown that the reliability of all-to-all broadcast can be improved considerably by employing the proposed network coding schemes, compared with non-coded networks with the same link conditions, i.e. same probabilities of successful packet transmission via wireless channels. Further, the proposed schemes take the link conditions of each node into account to maximise the reliability of a given network. To be more precise, the first scheme proposes the optimal coding neighbour selection method while the second scheme introduces a tuning parameter to control the probability that a node performs network coding at each transmission. The observation that channel condition can have a significant impact on the performance of network coding schemes is expected to be applicable to other network coding schemes for lossy wireless networks

Analysing and reducing the limitations of continuous-variable quantum cryptography and quantum networks

Due to a recent influx of attention, the field of quantum information is rapidly progressing towards the point at which quantum technologies move from the laboratory to widespread community use. However, several difficulties must be overcome before this milestone can be achieved. Two such difficulties are addressed in this thesis. The first is the ever-growing security threat posed by quantum computers to existing cryptographic protocols and the second is the missing knowledge regarding the performance differences between quantum and classical communications over various existing network topologies. Continuous-variable (CV) quantum key distribution (QKD) poses a practical solution to the security risks implied by the advancement of quantum information theory, with the promise of provably secure communications. Unfortunately, the maximum range of many CV-QKD protocols is limited. Here, this limitation is addressed by the application of post-selection, firstly, to a scenario in which two parties communicate using terahertz frequency radiation in the atmosphere, and secondly, to measurement-device-independent QKD, in which two parties communicate through the medium of an untrusted relay. In both cases, the introduction of post-selection enables security over distances substantially exceeding those of equivalent existing protocols. The second difficulty is addressed by a comparison of the quantum and classical networking regimes of the butterfly network and a group of networks constructed with butterfly blocks. By computing the achievable classical rates and upper bounds for quantum communication, the performance difference between the two regimes is quantified, and a range of conditions is established under which classical networking outperforms its quantum counterpart. This allows for guidance to be provided on which network structures should be avoided when constructing a quantum internet