Performance Analysis of Random Linear Network Coding in Two-Source Single-Relay Networks

This paper considers the multiple-access relay channel in a setting where two source nodes transmit packets to a destination node, both directly and via a relay node, over packet erasure channels. Intra-session network coding is used at the source nodes and inter-session network coding is employed at the relay node to combine the recovered source packets of both source nodes. In this work, we investigate the performance of the network-coded system in terms of the probability that the destination node will successfully recover the source packets of the two source nodes. We build our analysis on fundamental probability expressions for random matrices over finite fields and we derive upper bounds on the system performance for the case of systematic and non-systematic network coding. Simulation results show that the upper bounds are very tight and accurately predict the decoding probability at the destination node. Our analysis also exposes the clear benefits of systematic network coding at the source nodes compared to non-systematic transmission.Comment: Proc. ICC 2015, Workshop on Cooperative and Cognitive Mobile Networks (CoCoNet), to appea

Novel performance analysis of network coded communications in single-relay networks

In this paper, we analyze the performance of a single-relay network in which the reliability is provided by means of Random Linear Network Coding (RLNC). We consider a scenario when both source and relay nodes can encode packets. Unlike the traditional approach to relay networks, we introduce a passive relay mode, in which the relay node simply retransmits collected packets in case it cannot decode them. In contrast with the previous studies, we derive a novel theoretical framework for the performance characterization of the considered relay network. We extend our analysis to a more general scenario, in which coding coefficients are generated from non-binary fields. The theoretical results are verified using simulation, for both binary and non-binary fields. It is also shown that the passive relay mode significantly improves the performance compared with the active-only case, offering an up to two-fold gain in terms of the decoding probability. The proposed framework can be used as a building block for the analysis of more complex network topologies.Comment: Proceedings of IEEE GLOBECOM 2016 Communication Theory Symposium, to appea

Characterisation and performance analysis of random linear network coding for reliable and secure communication

In this thesis, we develop theoretical frameworks to characterize the performance of Random Linear Network Coding (RLNC), and propose novel communication schemes for the achievement of both reliability and security in wireless networks. In particular, (i) we present an analytical model to evaluate the performance of practical RLNC schemes suitable for low-complexity receivers, prioritized (i.e., layered) coding and multi-hop communications, (ii) investigate the performance of RLNC in relay assisted networks and propose a new cross-layer RLNC-aided cooperative scheme for reliable communication, (iii) characterize the secrecy feature of RLNC and propose a new physical-application layer security technique for the purpose of achieving security and reliability in multi-hope communications. At first, we investigate random block matrices and derive mathematical expressions for the enumeration of full-rank matrices that contain blocks of random entries arranged in a diagonal, lower-triangular or tri-diagonal structure. The derived expressions are then used to model the probability that a receiver will successfully decode a source message or layers of a service, when RLNC based on non-overlapping, expanding or sliding generations is employed. Moreover, the design parameters of these schemes allow to adjust the desired decoding performance. Next, we evaluate the performance of Random Linear Network Coded Cooperation (RLNCC) in relay assisted networks, and propose a cross-layer cooperative scheme which combines the emerging Non-Orthogonal Multiple Access (NOMA) technique and RLNCC. In this regard, we first consider the multiple-access relay channel in a setting where two source nodes transmit packets to a destination node, both directly and via a relay node. Secondly, we consider a multi-source multi-relay network, in which relay nodes employ RLNC on source packets and generate coded packets. For each network, we build our analysis on fundamental probability expressions for random matrices over finite fields and we derive theoretical expressions of the probability that the destination node will successfully decode the source packets. Finally, we consider a multi-relay network comprising of two groups of source nodes, where each group transmits packets to its own designated destination node over single-hop links and via a cluster of relay nodes shared by both groups. In an effort to boost reliability without sacrificing throughput, a scheme is proposed whereby packets at the relay nodes are combined using two methods; packets delivered by different groups are mixed using non-orthogonal multiple access principles, while packets originating from the same group are mixed using RLNC. An analytical framework that characterizes the performance of the proposed scheme is developed, and benchmarked against a counterpart scheme that is based on orthogonal multiple access. Finally, we quantify and characterize the intrinsic security feature of RLNC and design a joint physical-application layer security technique. For this purpose, we first consider a network comprising a transmitter, which employs RLNC to encode a message, a legitimate receiver, and a passive eavesdropper. Closed-form analytical expressions are derived to evaluate the intercept probability of RLNC, and a resource allocation model is presented to further minimize the intercept probability. Afterward, we propose a joint RLNC and opportunistic relaying scheme in a multi relay network to transmit confi- dential data to a destination in the presence of an eavesdropper. Four relay selection protocols are studied covering a range of network capabilities, such as the availability of the eavesdropper’s channel state information or the possibility to pair the selected relay with a jammer node that intentionally generates interference. For each case, expressions of the probability that a coded packet will not be decoded by a receiver, which can be either the destination or the eavesdropper, are derived. Based on those expressions, a framework is developed that characterizes the probability of the eavesdropper intercepting a sufficient number of coded packets and partially or fully decoding the confidential data. We observe that the field size over which RLNC is performed at the application layer as well as the adopted modulation and coding scheme at the physical layer can be modified to fine-tune the trade-off between security and reliability

Capacity of wireless erasure networks

In this paper, a special class of wireless networks, called wireless erasure networks, is considered. In these networks, each node is connected to a set of nodes by possibly correlated erasure channels. The network model incorporates the broadcast nature of the wireless environment by requiring each node to send the same signal on all outgoing channels. However, we assume there is no interference in reception. Such models are therefore appropriate for wireless networks where all information transmission is packetized and where some mechanism for interference avoidance is already built in. This paper looks at multicast problems over these networks. The capacity under the assumption that erasure locations on all the links of the network are provided to the destinations is obtained. It turns out that the capacity region has a nice max-flow min-cut interpretation. The definition of cut-capacity in these networks incorporates the broadcast property of the wireless medium. It is further shown that linear coding at nodes in the network suffices to achieve the capacity region. Finally, the performance of different coding schemes in these networks when no side information is available to the destinations is analyzed

Whether and Where to Code in the Wireless Relay Channel

The throughput benefits of random linear network codes have been studied extensively for wirelined and wireless erasure networks. It is often assumed that all nodes within a network perform coding operations. In energy-constrained systems, however, coding subgraphs should be chosen to control the number of coding nodes while maintaining throughput. In this paper, we explore the strategic use of network coding in the wireless packet erasure relay channel 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. In addition to transmission energy, we take into account coding and reception energies. We show that coding at the relay alone while operating in a rateless fashion is neither throughput nor energy efficient. Given a set of system parameters, our analysis determines the optimal amount of time the relay should participate in the transmission, and where coding should be performed.Comment: 11 pages, 12 figures, to be published in the IEEE JSAC Special Issue on Theories and Methods for Advanced Wireless Relay

Doped Fountain Coding for Minimum Delay Data Collection in Circular Networks

This paper studies decentralized, Fountain and network-coding based strategies for facilitating data collection in circular wireless sensor networks, which rely on the stochastic diversity of data storage. The goal is to allow for a reduced delay collection by a data collector who accesses the network at a random position and random time. Data dissemination is performed by a set of relays which form a circular route to exchange source packets. The storage nodes within the transmission range of the route's relays linearly combine and store overheard relay transmissions using random decentralized strategies. An intelligent data collector first collects a minimum set of coded packets from a subset of storage nodes in its proximity, which might be sufficient for recovering the original packets and, by using a message-passing decoder, attempts recovering all original source packets from this set. Whenever the decoder stalls, the source packet which restarts decoding is polled/doped from its original source node. The random-walk-based analysis of the decoding/doping process furnishes the collection delay analysis with a prediction on the number of required doped packets. The number of doped packets can be surprisingly small when employed with an Ideal Soliton code degree distribution and, hence, the doping strategy may have the least collection delay when the density of source nodes is sufficiently large. Furthermore, we demonstrate that network coding makes dissemination more efficient at the expense of a larger collection delay. Not surprisingly, a circular network allows for a significantly more (analytically and otherwise) tractable strategies relative to a network whose model is a random geometric graph

Systematic Network Coding with the Aid of a Full-Duplex Relay

A characterization of systematic network coding over multi-hop wireless networks is key towards understanding the trade-off between complexity and delay performance of networks that preserve the systematic structure. This paper studies the case of a relay channel, where the source's objective is to deliver a given number of data packets to a receiver with the aid of a relay. The source broadcasts to both the receiver and the relay using one frequency, while the relay uses another frequency for transmissions to the receiver, allowing for a full-duplex operation of the relay. We analyze the decoding complexity and delay performance of two types of relays: one that preserves the systematic structure of the code from the source; another that does not. A systematic relay forwards uncoded packets upon reception, but transmits coded packets to the receiver after receiving the first coded packet from the source. On the other hand, a non-systematic relay always transmits linear combinations of previously received packets. We compare the performance of these two alternatives by analytically characterizing the expected transmission completion time as well as the number of uncoded packets forwarded by the relay. Our numerical results show that, for a poor channel between the source and the receiver, preserving the systematic structure at the relay (i) allows a significant increase in the number of uncoded packets received by the receiver, thus reducing the decoding complexity, and (ii) preserves close to optimal delay performance.Comment: 6 pages, 5 figures, submitted to IEEE Globeco