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Delay Bounds for random linear coding in Parallel Relay Networks

IEEE TRANSACTIONS ON MOBILE COMPUTING 2015年第5期14卷 964-974页

作者： Cogill, Randy Shrader, Brooke IBM Res Ireland Dublin 15 Ireland MIT Lincoln Lab Lexington MA 02420 USA

We consider the problem of transmitting a collection of packets from a source node to a destination node across a relay network. We analyze a simple random network coding scheme where each node transmits a random linear combination of packets each time it has an opportunity to transmit. The main result of this paper is an upper bound on the expected time to transmit a generation of packets across the network. We show that the expected time is bounded by the generation size divided by the capacity of the minimum cut separating the source from the destination, plus a term that grows as the square root of the generation size. We then use this bound to provide a queueing analysis of a strategy that dynamically creates generations as packets arrive in a queue at the network's source node. To facilitate our analysis, we model the relay network by a continuous-time Markov chain. Our primary analytical tool is a general method for computing upper bounds on hitting times associated with continuous-time Markov chains. We believe that this approach also provides a method for analyzing transmission times associated with more general network topologies.

关键词： Delay random linear coding network coding erasure network relay network queueing analysis continuous-time Markov chains

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Providing Reliable Services over Wireless Networks Using a Low Overhead random linear coding Scheme

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MOBILE NETWORKS & APPLICATIONS 2017年第6期22卷 1113-1123页

作者： Garrido, Pablo Gomez, David Lanza, Jorge Serrat, Joan Aguero, Ramon Univ Cantabria Santander Spain Univ Politecn Cataluna Barcelona Spain

In this work, we propose a novel intra-flow network coding solution, which is based on the combination of a low overhead random linear coding (RLC) scheme and UDP, to offer a reliable communication service. In the initial protocol specification, the required overhead could be rather large and this had an impact over the observed performance. We therefore include an improvement to reduce such overhead, by decreasing the header length. We describe an analytical model that can be used to assess the performance of the proposed scheme. We also use an implementation within the ns-3 framework to assess the correctness of this model and to broaden the analysis, considering different performance indicators and more complex network topologies. In all cases, the proposed solution clearly outperforms a more traditional approach, in which the TCP protocol is used as a means to offer a reliable communication service.

关键词： random linear coding Wireless networks IEEE 802.11 Protocol overhead Packets erasure channels Load balance control

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Unequal Error Protection random linear coding Strategies for Erasure Channels

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IEEE TRANSACTIONS ON COMMUNICATIONS 2012年第5期60卷 1243-1252页

作者： Vukobratovic, Dejan Stankovic, Vladimir Univ Novi Sad Dept Power Elect & Commun Engn Novi Sad 21000 Serbia Univ Strathclyde Dept Elect & Elect Engn Glasgow G1 1XW Lanark Scotland

In this paper, we provide the performance analysis of unequal error protection (UEP) random linear coding (RLC) strategies designed for transmission of source messages containing packets of different importance over lossy packet erasure links. By introducing the probabilistic encoding framework, we first derive the general performance limits for the packet-level UEP coding strategies that encode the packets of each importance class of the source message independently (non-overlapping windowing strategy) or jointly (expanding windowing strategy). Then, we demonstrate that the general performance limits of both strategies are achievable by the probabilistic encoding over non-overlapping and expanding windows based on RLC and the Gaussian Elimination (GE) decoding. Throughout the paper, we present a number of examples that investigate the performance and optimization of code design parameters of the expanding window RLC strategy and compare it with the non-overlapping RLC strategy selected as a reference.

关键词： Network coding random linear coding unequal error protection

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Stable Throughput for Multicast With random linear coding

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IEEE TRANSACTIONS ON INFORMATION THEORY 2011年第1期57卷 267-281页

作者： Cogill, Randy Shrader, Brooke Ephremides, Anthony Univ Virginia Dept Syst & Informat Engn Charlottesville VA 22904 USA MIT Lincoln Lab Lexington MA 02420 USA Univ Maryland Dept Elect & Comp Engn College Pk MD 20742 USA

This paper compares scheduling and coding strategies for a multicast version of a classic downlink problem. We consider scheduling strategies where, in each time slot, a scheduler observes the lengths of all queues and the connectivities of all links and can transmit the head-of-the-line packet from a single queue. We juxtapose this to a coding strategy that is simply a form of classical random linear coding. We show that there are configurations for which the stable throughput region of the scheduling strategy is a strict subset of the corresponding throughput region of the coding strategy. This analysis is performed for both time-invariant and time-varying channels. The analysis is also performed both with and without accounting for the impact on throughput of including coding overhead symbols in each encoded packet. Additionally, we compare coding strategies that only code within individual queues against a coding strategy that codes across separate queues. The strategy that codes across queues simply sends packets from all queues to all receivers. As a result, this strategy sends many packets to unnecessary recipients. We show, surprisingly, that there are cases where the strategy that codes across queues can achieve the same throughput region achievable by coding within individual queues.

关键词： Cross-layer control multicast queueing systems random linear coding wireless networks

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Performance of random linear coding Over Multiple Error-Prone Wireless Links

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IEEE COMMUNICATIONS LETTERS 2015年第6期19卷 1033-1036页

作者： Garrido, Pablo Gomez, David Agueero, Ramon Munoz, Luis Univ Cantabria Commun Engn Dept E-39005 Santander Spain

In this letter we derive an exact formulation for the performance of random linear coding (RLC) when applied over multiple wireless links. We combine this technique with UDP so as to offer a reliable communication service. We extend a previous result, which only considered one single link, to embrace both multiple sources as well as varying quality of wireless links. We establish the number of excess packets that are required to successfully accomplish the communication and, based on the Bianchi model, we calculate the achieved throughput. We also propose a context-aware probabilistic transmission scheme that leads to a relevant performance gain. We use a thorough simulation-based study over the ns-3 framework to assess the validity of the proposed model and to broaden the corresponding analysis.

关键词： random linear coding wireless mesh networks simulation

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The Explicit Decoding Delay Probability Distribution Based on random linear coding Scheme

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IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES 2013年第11期E96A卷 2299-2301页

作者： Zhao, Xubo Zhou, Hang Li, Xiaoping China Univ Petr Coll Sci Qingdao 266580 Shandong Peoples R China Xidian Univ ISN State Key Lab Xian 710071 Shanxi Peoples R China Univ Chinese Peoples Armed Police Force Xian 710086 Peoples R China

Under random linear coding (RLC) scheme, we present a simple expression of the probability distribution p(D = K) for decoding delay D incurred by the lossy channel, where K is a positive integer. In contrast with the previous contribution, our focus is firstly on deriving the cumulative distribution function of the discrete random variable D over a perfect channel. One benefit of such dispose is that, from the overall viewpoint, computing the cumulative distribution function of delay D can be related with calculating the cardinalities of sets of some special matrices, so that the former can be obtained from the latter. Moreover, our expression of the probability distribution is an explicit form, and is valid for any number of packets M, freewill field size q and arbitrary channel loss rate epsilon.

关键词： random linear coding lossy channel decoding delay

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A New Method for the Decoding Delay Distributions of random linear coding Schemes

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IEEE COMMUNICATIONS LETTERS 2017年第2期21卷 226-229页

作者： Zhao, Xubo Li, Xiaoping Yan, Tongjiang Shi, Rengang China Univ Petr Huadong Coll Sci Qingdao 266580 Peoples R China Fujian Normal Univ Fujian Prov Key Lab Network Secur & Cryptol Fuzhou 350007 Peoples R China

In this letter, we introduce a new technique for deriving the exact decoding delay distribution expressions of random linear coding schemes over a lossy channel. Our approach is mainly based on two transformations: on the one hand, from an overall perspective, the correspondence between the calculation of the exact decoding delay distribution over a perfect channel and the counting problem for some special matrices can be established. On the other hand, the relationship between some cardinalities of the special matrices and the typical basis of polynomials can be obtained. Last, the decoding delay distribution issues can be solved by employing the polynomial basis representation method.

关键词： random linear coding decoding delay probability distribution lossy channel

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Queueing Delay Analysis for Multicast With random linear coding

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IEEE TRANSACTIONS ON INFORMATION THEORY 2012年第1期58卷 421-429页

作者： Shrader, Brooke Ephremides, Anthony MIT Lincoln Lab Lexington MA 02421 USA Univ Maryland Dept Elect & Comp Engn College Pk MD 20742 USA Univ Maryland Syst Res Inst College Pk MD 20742 USA

We analyze the queueing delay performance when random linear coding is performed over packets randomly arriving at a source node for multicast transmission over packet erasure channels. We model random coding of packets as a bulk-service queueing system, where packets are served and depart the queue in groups. In this framework, we analyze two different block-based random linear coding schemes. The first scheme involves coding over a fixed blocksize, which leads to simpler analysis but also to a delay penalty for lightly-loaded systems. The second scheme adapts to the traffic load by allowing for a variable blocksize, thereby removing the delay penalty at low loads. We provide results on the maximum stable arrival rate of packets at the source and on the queueing delay as a function of the arrival rate.

关键词： Buffering bulk service delay erasure channel multicast network coding queueing random linear coding wireless networks

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Multicast Queueing Delay: Performance Limits and Order-Optimality of random linear coding

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IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS 2011年第5期29卷 1075-1083页

作者： Cogill, Randy Shrader, Brooke Univ Virginia Dept Syst & Informat Engn Charlottesville VA 22904 USA MIT Lincoln Lab Lexington MA 02420 USA

In this work we analyze the average queue backlog for transmission of a single multicast flow consisting of M destination nodes in a wireless network. In the model we consider, the channel between every pair of nodes is an independent identically distributed packet erasure channel. We first develop a lower bound on the average queue backlog achievable by any transmission strategy;for a single-hop multicast transmission, our bound indicates that the queue size must scale as at least Omega(ln(M)). Next, we generalize this result to a multihop network and obtain a lower bound on the queue backlog as it relates to the minimum-cut capacity of the network. We then analyze the queue backlog for a strategy in which random linear coding is performed over groups of packets in the queue at the source node of a single-hop multicast. We develop an upper bound on the average queue backlog for the packet-coding strategy to show that the queue size for this strategy scales as O(ln(M)). Our results demonstrate that in terms of the queue backlog for single-hop multicast, the packet coding strategy is order-optimal with respect to the number of receivers.

关键词： multicast queue backlog queueing delay random linear coding packet coding packet erasure network min-cut capacity

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Lightweight random linear coding over Wireless Mesh Networks 7th

Lightweight Random Linear Coding over Wireless Mesh Networks

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7th EAI International Conference on Mobile Networks and Management (MONAMI)

作者： Garrido, Pablo Gomez, David Lanza, Jorge Agueero, Ramon Serrat, Joan Univ Cantabria E-39005 Santander Spain Univ Politecn Cataluna Barcelona Spain

ISBN: (纸本)9783319269252;9783319269245

We propose an enhanced version of an intra-flow Network coding protocol, which was conceived to offer a reliable communication service, by means of the combination a random linear coding (RLC) scheme with the UDP protocol. We reduce the overhead that was originally required in the protocol header and we assess, through an extensive campaign carried out over the ns-3 framework, the performance gain that is brought by this enhancement, comparing it to the TCP protocol, as the mainstream transport-level solution to offer a reliable service. We study the impact of the various configuration parameters of the solution. Afterwards, we challenge the proposed scheme over random topologies (Wireless Mesh Networks or WMNs). The results show a remarkable gain (approximately 20 times higher) of the performance over an ideal channel, thanks to the aforementioned overhead reduction.

关键词： random linear coding Network coding Simulation Wireless mesh networks

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