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decoding probability in Random Linear Network Coding with Packet Losses

IEEE COMMUNICATIONS LETTERS 2013年第11期17卷 2128-2131页

作者： Chiasserini, Carla-Fabiana Viterbo, Emanuele Casetti, Claudio Politecn Torino Turin Italy Monash Univ ECSE Clayton Vic 3800 Australia

We focus on a network where n sources send data to k destinations, through m >= n relay nodes employing random linear network coding. The coefficients used to encode the data packets are extracted from a Galois field of size q. Unlike previous work, we consider that the relay nodes may not receive some packets due to link failures. This implies that a destination may be unable to successfully decode the received data packets due to both missing packets at the relays and linearly dependent coefficient vectors. In this scenario, we compute the exact probability of successful decoding at a destination node and we show the impact of the system parameters on the performance. In particular, our study highlights the fact that the network coding scheme behaves as an erasure correcting code, whose erasure correcting capability is determined by the number of available relays.

关键词： Linear random network coding random matrices decoding probability

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Notes on "Exact decoding probability Under Random Linear Network Coding"

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IEEE COMMUNICATIONS LETTERS 2012年第5期16卷 720-721页

作者： Zhao, Xubo Xidian Univ State Key Lab Integrated Serv Networks Xian 710071 Peoples R China China Univ Petr Coll Sci Qingdao Peoples R China

In a recent letter, Trullols-Cruces et al. derived the exact decoding probability P-ns(K, N) that a receiver node obtained N linearly independent coded packets among K (K >= N) received coded packets, when the source node uses a random linear coding scheme over a Galois Field GF(q). They discussed P-ns(K, N) both in the case of the source node sending the random linear combination of the original packets, including all-zero combinations, as well as the case of excluding all-zero combinations. However, their derivations are a bit complicated. In this note, we demonstrate simple derivations of the exact decoding probability P-ns(K, N) in both cases. Furthermore, we point out that there is a more succinct expression of P-ns(K, N) for the latter case.

关键词： Random linear coding wireless networks decoding probability

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On the decoding Failure probability of Random Network Coded Cooperation 89

On the Decoding Failure Probability of Random Network Coded ...

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89th IEEE Vehicular Technology Conference (VTC Spring)

作者： Chatzigeorgiou, Ioannis Kurt, Gunes Basaran, Semiha Tedik Khan, Amjad Saeed Univ Lancaster Sch Comp & Commun Lancaster LA1 4WA England Istanbul Tech Univ Dept Elect & Commun Engn TR-34469 Istanbul Turkey Loughborough Univ Sch Mech Elect & Mfg Engn Loughborough LE11 3TU Leics England

ISBN: (纸本)9781728112176

This paper considers a network of source nodes that transmit data packets to a destination node via relay nodes over erasure channels by using random linear network coding. The probability that the destination node will fail to recover the packets of all source nodes has been bounded and approximated in the literature for the case of relay nodes that randomly assign only nonzero values to the coefficients of linear combinations of data packets. The paper argues for the necessity of giving relay nodes the choice to also assign the zero value to coefficients when arithmetic operations are over finite fields of small size, e.g. GF(2). Alternative probability mass functions for the coefficients are considered, and expressions for the decoding failure probability are re-derived.

关键词： Cooperative communication decoding probability random linear network coding random matrices

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Fulcrum: Flexible Network Coding for Heterogeneous Devices

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IEEE ACCESS 2018年 6卷 77890-77910页

作者： Lucani, Daniel E. Pedersen, Morten Videbaek Ruano, Diego Sorensen, Chres W. Fitzek, Frank H. P. Heide, Janus Geil, Olav Nguyen, Vu Reisslein, Martin Aarhus Univ DIGIT Ctr Dept Engn DK-8200 Aarhus Denmark Steinwurf ApS DK-9220 Aalborg Denmark Univ Valladolid Math Res Inst IMUVA E-47011 Valladolid Spain Aalborg Univ Dept Math Sci DK-9200 Aalborg Denmark Chocolate Cloud ApS DK-9220 Aalborg Denmark Tech Univ Dresden Deutsch Telekom Chair Commun Networks 5G Lab Germany D-01069 Dresden Germany Arizona State Univ Sch Elect Comp & Energy Engn Tempe AZ 85287 USA

We introduce Fulcrum, a network coding framework that achieves three seemingly conflicting objectives: 1) to reduce the coding coefficient overhead down to nearly n bits per packet in a generation of n packets;2) to conduct the network coding using only Galois field GF (2) operations at intermediate nodes if necessary, dramatically reducing computing complexity in the network;and 3) to deliver an end-to-end performance that is close to that of a high-field network coding system for high-end receivers, while simultaneously catering to low-end receivers that decode in GF (2). As a consequence of 1) and 3), Fulcrum has a unique trait missing so far in the network coding literature: providing the network with the flexibility to distribute computational complexity over different devices depending on their current load, network conditions, or energy constraints. At the core of our framework lies the idea of precoding at the sources using an expansion field GF(2(h));h > 1, to increase the number of dimensions seen by the network. Fulcrum can use any high-field linear code for precoding, e.g., Reed-Solomon or Random Linear Network Coding (RLNC). Our analysis shows that the number of additional dimensions created during precoding controls the trade-off between delay, overhead, and computing complexity. Our implementation and measurements show that Fulcrum achieves similar decoding probabilities as high field RLNC but with encoders and decoders that are an order of magnitude faster.

关键词： decoding probability random linear network coding (RLNC) resource-constrained devices throughput

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Network-Coded NOMA With Antenna Selection for the Support of Two Heterogeneous Groups of Users

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IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS 2019年第2期18卷 1332-1345页

作者： Khan, Amjad Saeed Chatzigeorgiou, Ioannis Lambotharan, Sangarapillai Zheng, Gan Loughborough Univ Wolfson Sch Mech Elect & Mfg Engn Loughborough LE11 3TU Leics England Univ Lancaster Sch Comp & Commun Lancaster LA1 4WA England

The combination of non-orthogonal multiple access (NOMA) and transmit antenna selection (TAS) techniques has recently attracted significant attention due to the low cost, low complexity, and high diversity gains. Meanwhile, random linear coding (RLC) is considered to be a promising technique for achieving high reliability and low latency in multicast communications. In this paper, we consider a downlink system with a multi-antenna base station and two multicast groups of single-antenna users, where one group can afford to be served opportunistically, while the other group consists of comparatively low-power devices with limited processing capabilities that have strict quality of service (QoS) requirements. In order to boost reliability and satisfy the QoS requirements of the multicast groups, we propose a cross-layer framework, including NOMA-based TAS at the physical layer and RLC at the application layer. In particular, two low-complexity TAS protocols for NOMA are studied in order to exploit the diversity gain and meet the QoS requirements. In addition, RLC analysis aims to facilitate heterogeneous users, such that sliding window-based sparse RLC is employed for computational restricted users, and conventional RLC is considered for others. Theoretical expressions that characterize the performance of the proposed framework are derived and verified through simulation results.

关键词： Antenna selection non-orthogonal multiple access network coding random block matrices outage probability decoding probability throughput

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Adaptive Network Coding for Broadband Wireless Access Networks

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IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS 2013年第1期24卷 4-18页

作者： Lin, Hui-Tang Lin, Ying-You Kang, Hung-Jung Natl Cheng Kung Univ Inst Comp & Commun Engn Tainan 701 Taiwan Natl Cheng Kung Univ Dept Elect Engn Tainan 701 Taiwan

Broadband wireless access (BWA) networks, such as LTE and WiMAX, are inherently lossy due to wireless medium unreliability. Although the Hybrid Automatic Repeat reQuest (HARQ) error-control method recovers from packet loss, it has low transmission efficiency and is unsuitable for delay-sensitive applications. Alternatively, network coding techniques improve the throughput of wireless networks, but incur significant overhead and ignore network constraints such as Medium Access Control (MAC) layer transmission opportunities and physical (PHY) layer channel conditions. The present study provides analysis of Random Network Coding (RNC) and Systematic Network Coding (SNC) decoding probabilities. Based on the analytical results, SNC is selected for developing an adaptive network coding scheme designated as Frame-by-frame Adaptive Systematic Network Coding (FASNC). According to network constraints per frame, FASNC dynamically utilizes either Modified Systematic Network Coding (M-SNC) or Mixed Generation Coding (MGC). An analytical model is developed for evaluating the mean decoding delay and mean goodput of the proposed FASNC scheme. The results derived using this model agree with those obtained from computer simulations. Simulations show that FASNC results in both lower decoding delay and reduced buffer requirements compared to MRNC and N-in-1 ReTX, while also yielding higher goodput than HARQ, MRNC, and N-in-1 ReTX.

关键词： Retransmission MAC layer network coding next generation broadband wireless access networks decoding delay decoding probability

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Hierarchical secret image sharing scheme in compressed sensing

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SIGNAL PROCESSING-IMAGE COMMUNICATION 2018年 61卷 21-32页

作者： Bhattacharjee, Tapasi Maity, Santi P. Islam, Sheikh Rafiul Indian Inst Engn Sci & Technol Dept Informat Technol PO Bot Garden Sibpur 711103 Howrah India

Secret image sharing (SIS) is a technique of protecting the secret images from an unauthorized access through the generation of few shares or shadow images and serves various purposes such as multi-party computation, threshold cryptography, access control etc. Some of these applications demand hierarchical access based SIS scheme with flexible shadow size adaptive to the available transmission bandwidth. To this aim, share/shadow image generation (with reduced size) is considered here as a sparse signal (secret) reconstruction problem as is done in compressed sensing or compressive sampling (CS). A prediction error (PE) matrix is formed for the secret image which then undergoes sub-sampling followed by its partitioning into two sets of shares: one mandatory share (MS) and 'n' number of general shares (GSs) thus form an integrated framework of CS and Shamir's (k, n) threshold secret sharing scheme. The contribution of the MS and at least 'k' number of GSs are essential to reconstruct the secret image. The change in the number of CS measurements leads to the flexibility in share size adaptive to transmission bandwidth and offers a progressive quality access control along with relative changes in unauthorized decoding probability. A large set of simulation results show the average decoding quality of the secret images with PSNR values of 31.4 dB and 35.7 dB for 10% and 30% measurements, respectively. (C) 2017 Elsevier B.V. All rights reserved.

关键词： Secret image sharing Prediction error Compressed sensing Access control Kullback-Leibler divergence decoding probability

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Non-Orthogonal Multiple Access Combined With Random Linear Network Coded Cooperation

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IEEE SIGNAL PROCESSING LETTERS 2017年第9期24卷 1298-1302页

作者： Khan, Amjad Saeed Chatzigeorgiou, Ioannis Univ Lancaster Sch Comp & Communcat Lancaster LA1 4WA England

This letter considers two groups of source nodes. 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 random linear network coding. An analytical framework that characterizes the performance of the proposed scheme is developed, compared to simulation results, and benchmarked against a counterpart scheme that is based on orthogonal multiple access.

关键词： decoding probability network coding nonorthogonal multiple access (NOMA) sparse random matrices throughput

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

Performance Analysis of Random Linear Network Coding in Two-...

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IEEE International Conference on Communications (ICC)

作者： Khan, Amjad Saeed Chatzigeorgiou, Ioannis Univ Lancaster Sch Comp & Commun Lancaster LA1 4YW England

ISBN: (纸本)9781467363051

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.

关键词： Network coding fountain coding multiple access relay channel decoding probability block angular matrix

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Efficient Communication over Cellular Networks with Network Coding in Emergency Scenarios 2

Efficient Communication over Cellular Networks with Network ...

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2nd International Conference on Information and Communication Technologies for Disaster Management (ICT-DM)

作者： Do-Duy, Tan Vazquez-Castro, M. A. Autonomous Univ Barcelona Dept Telecommun & Syst Engn E-08193 Barcelona Spain

ISBN: (纸本)9781479999231

Emergency communications require reliability and flexibility for disaster recovery and relief operation. Based upon existing commercial portable devices (e.g., smartphones, tablets, laptops), we propose a network architecture that uses cellular networks and WiFi connections to deliver large files (e.g. detailed maps) in emergency scenarios under the impairments of wireless channel such as packet losses and intermittent connection. Network coding (NC) is exploited to improve the delivery probability beyond cellular coverage. We first review the state-of-the-art of NC for emergency communications. Then, we present the proposed network architecture which utilizes multiple radio interfaces of portable devices to support data delivery. A random linear NC scheme is exploited both at the source and intermediate nodes, and an analytical model for the successful decoding probability is derived. Finally, we evaluate the effectiveness of the proposed architecture with NC in terms of the delivery ratio of content for intermittent connectivity scenarios.

关键词： Network coding cellular networks emergency communications decoding probability coverage extension

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