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Dualities between entropy functions and network codes

IEEE TRANSACTIONS ON INFORMATION theory 2008年第10期54卷 4470-4487页

作者： Chan, Terence Grant, Alex Univ S Australia Inst Telecommun Res Adelaide SA 5095 Australia

In communications networks, the capacity region of multisource network coding is given in terms of the set of entropy functions Gamma*. More broadly, determination of Gamma* would have an impact on converse theorems for multi-terminal problems in information theory. this paper provides several new dualities between entropy functions and network codes. Given a function g >= 0 defined on all subsets of N random variables, we provide a construction for a network multicast problem which is "solvable" if and only if g is the entropy function of a set of quasi-uniform random variables. the underlying network topology is fixed and the multicast problem depends on g only through link capacities and source rates. A corresponding duality is developed for linear network codes, where the constructed multicast problem is linearly solvable if and only if g is linear group characterizable. Relaxing the requirement that the domain of g be subsets of random variables, we obtain a similar duality between polymatroids and the linear programming bound. these duality results provide an alternative proof of the insufficiency of linear (and abelian) network codes, and demonstrate the utility of non-Shannon inequalities to tighten outer bounds on network coding capacity regions.

关键词： duality entropy functions Ingleton's inequality LP bounds network codes polymatroids pseudovariables

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On locating Byzantine attackers

On locating Byzantine attackers

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4th workshop on network coding, theory and applications

作者： Siavoshani, Mahdi Jafari Fragouli, Christina Diggavi, Suhas Ecole Polytech Fed Lausanne Sch Comp & Commun Sci Lausanne Switzerland

ISBN: (纸本)9781424416899

We examine networks that employ network coding and are subject to Byzantine attacks. We assume that an appropriate network error correcting scheme is employed that is able to correct (up to a certain number of) Byzantine errors. Given this setup, we formulate the problem of locating these malicious nodes that insert errors. We utilize the subspace properties of (randomized) network coding to develop algorithms to locate the Byzantine attackers.

关键词： network coding

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Online broadcasting with network coding

Online broadcasting with network coding

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4th workshop on network coding, theory and applications

作者： Keller, Lorenzo Drinea, Eleni Fragouli, Christina Ecole Polytech Fed Lausanne Dept Commun Syst CH-1015 Lausanne Switzerland

Consider a source broadcasting M packets to N receivers over independent erasure channels, where perfect feedback is available from the receivers to the source, and the source is allowed to use coding. We investigate ... 详细信息

ISBN: (纸本)9781424416899

关键词： Signal receivers

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A graham-sloane type construction of constant dimension codes

A graham-sloane type construction of constant dimension code...

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4th workshop on network coding, theory and applications

作者： Xia, Shu-Tao Tsing Hua Univ Grad Sch Shenzhen Shenzhen 518055 Guangdong Peoples R China

ISBN: (纸本)9781424416899

Very recently, an operator channel was defined by Koetter and Kschischang when they studied random network coding. they also introduced constant dimension codes and demonstrated that these codes can be employed to correct errors and/or erasures over the operator channel. In this paper, a Graham-Sloane type construction of constant dimension codes is presented. It is shown that the construction for the case of minimum dimension distance 4 exceeds the Gilbert type lower bound for constant dimension codes.

关键词： network coding

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Rainbow network flow with network coding

Rainbow network flow with network coding

引用

4th workshop on network coding, theory and applications

作者： Shao, Mingkai Wu, Xiaolin Sarshar, Nima McMaster Univ Dept Elect & Comp Engn Hamilton ON Canada Univ Regina Dept Software Syst Engn Regina SK S4S 0A2 Canada

ISBN: (纸本)9781424416899

Rainbow network flow is a recent enquiry into rate-distortion optimized network flow of a multiple description (MD) coded source from multiple encoders to multiple sinks. this paper is a first attempt to combine network coding with rainbow network flow, and formulates a new problem called rainbow network coding (RNC). It is shown that performing linear network coding at intermediate nodes of a flow path can achieve higher network throughput than the original rainbow network flow solution. RNC is related to the linear broadcast problem defined in network coding theory, but it has a different objective function that is more meaningful for lossy signal compression applications than linear broadcast. We prove the RNC problem to be NP-hard, and propose some heuristic solutions. Examples are presented to study the differences between rainbow network coding, rainbow network flow, and linear broadcast.

关键词： network coding

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Opportunistic cooperative network-coding based on space-time coding for bi-directional traffic flows

Opportunistic cooperative network-coding based on space-time...

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2008 4th workshop on network coding, theory, and applications, NetCod 2008

作者： Ling, Lv Hongyi, Yu Jianzu, Yang Dept. of Communication Engineering Inf. Science and Technology Institute Zhengzhou Henan Province China

ISBN: (纸本)9781424416899

In multi-hop wireless networks, network coding can take advantage of the bi-directional traffic flows to increase the achievable throughput. To combat fading in wireless channel, cooperative diversity is integrated into the network-coding schemes. In this paper, we propose an opportunistic cooperative network-coding scheme based on space-time coding (OCNC), which combats channel fading and improves resource efficiency and network throughput. Focusing on the bi-directional traffic flows in wireless cooperative relaying networks, we develop and analyze the outage probabilities and the network-coding gain of different bi-directional relaying schemes. the numerical results show that in contrast to traditional scheme both full diversity (i.e. k-order diversity in case of K relay nodes) and asymptotical 4/3 times of network-coding gain are achieved by OCNC. In addition, because of opportunistic relaying of multiple nodes, the network-coding gain is more considerable in the low and middle SNR regimes. © 2008 IEEE.

关键词： network coding

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Dualities between entropy functions and network codes

Dualities between entropy functions and network codes

引用

4th workshop on network coding, theory and applications

作者： Chan, Terence Grant, Alex Univ S Australia Inst Telecommun Res Adelaide SA 5095 Australia

ISBN: (纸本)9781424416899

关键词： duality entropy functions Ingleton's inequality LP bounds network codes polymatroids pseudovariables

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network coding meets MIMO

Network coding meets MIMO

引用

4th workshop on network coding, theory and applications

作者： Fasolo, Elena Rossetto, Francesco Zorzi, Michele Univ Padua DEI Via G Gradenigo 6-B I-35131 Padua Italy

ISBN: (纸本)9781424416899

In this paper, MIMO techniques are applied to network coding in order to exploit the spatial diversity inherent in packet combining. this is possible because network coding and MIMO solve similar problems, namely to decode a vector of transmitted symbols given a vector of received samples. this observation leads to a new approach for NC coding/decoding. Our basic idea is to move network coding functionalities towards the physical layer in order to jointly perform NC decoding and MIMO detection and gain the advantages of the two approaches. We refer to this new strategy as MIMO_NC. theoretical analysis and simulations prove that our system is more robust than traditional network coding to fading and packet losses.

关键词： network coding

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Optimal layered multicast using network coding

Optimal layered multicast using network coding

引用

4th workshop on network coding, theory and applications

作者： Si Jingjing Zhuang Bojin Cai Anni Beijing Univ Posts & Telecommun Sch Telecom Engn Beijing 100088 Peoples R China

ISBN: (纸本)9781424416899

We investigate the problem of constructing optimal layered multicast for heterogeneous sink nodes using network coding. Taking the flexibility of layered coding into account, we discuss the optimization problem that determines the optimal layers' bit-rates for layered multicast, and express it into a mathematical formulation. Finding that this formulation is nonlinear and difficult to solve, we reduce it into several equivalent optimization problems and further propose a new optimization scheme. Different from the min-favorable algorithm in existing work, this new scheme is a global-favorable one, which determines the optimal layers' bit-rates based on the max-flows of all sink nodes. Simulation results indicate that this new scheme could achieve the maximum of the aggregate throughput for layered multicast.

关键词： network coding throughput Multicast algorithms Resource management Aggregates Computer networks Telecommunication network reliability Polynomials Cost function Delay

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A concatenated network coding scheme for multimedia transmission

A concatenated network coding scheme for multimedia transmis...

引用

4th workshop on network coding, theory and applications

作者： Walsh, John MacLaren Weber, Steven Drexel Univ Dept Elect & Comp Engn Philadelphia PA 19104 USA

ISBN: (纸本)9781424416899

We discuss a coding technique for transmitting temporally ordered and/or successive refinements encoded multimedia data (such as MPEG video) over a multi-cast network using recently developed breakthrough network coding techniques. Hybridizing network coding philosophy with that of priority encoded transmission and fountain codes, we provide a method which allows a sink to forward to higher OSI model layers (i.e. the source decoder lying in the application layer) the uncoded source data in order of importance as the network coded packets arrive. this technique avoids the delay presently incurred by waiting for the reception of a full rank network coding matrix before decoding the entire block and forwarding it to higher layers.

关键词： network coding

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