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Network Coding Fundamentals
 FOUNDATIONS AND TRENDS IN NETWORKING
, 2007
"... Network coding is an elegant and novel technique introduced at the turn of the millennium to improve network throughput and performance. It is expected to be a critical technology for networks of the future. This tutorial addresses the first most natural questions one would ask about this new techni ..."
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Cited by 48 (10 self)
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Network coding is an elegant and novel technique introduced at the turn of the millennium to improve network throughput and performance. It is expected to be a critical technology for networks of the future. This tutorial addresses the first most natural questions one would ask about this new technique: how network coding works and what are its benefits, how network codes are designed and how much it costs to deploy networks implementing such codes, and finally, whether there are methods to deal with cycles and delay that are present in all real networks. A companion issue deals primarily with applications of network coding.
Utility Maximization in PeertoPeer Systems
"... In this paper, we study the problem of utility maximization in P2P systems, in which aggregate applicationspecific utilities are maximized by running distributed algorithms on P2P nodes, which are constrained by their uplink capacities. This may be understood as extending Kelly’s seminal framework f ..."
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Cited by 43 (12 self)
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In this paper, we study the problem of utility maximization in P2P systems, in which aggregate applicationspecific utilities are maximized by running distributed algorithms on P2P nodes, which are constrained by their uplink capacities. This may be understood as extending Kelly’s seminal framework from singlepath unicast over general topology to multipath multicast over P2P topology, with network coding allowed. For certain classes of popular P2P topologies, we show that routing along a linear number of trees per source can achieve the largest rate region that can be possibly obtained by (multisource) network coding. This simplification result allows us to develop a new multitree routing formulation for the problem. Despite of the negative results in literature on applying Primaldual algorithms to maximize utility under multipath settings, we have been able to develop a Primaldual distributed algorithm to maximize the aggregate utility under the multipath routing environments. Utilizing our proposed sufficient condition, we show global exponential convergence of the Primaldual algorithm to the optimal solution under different P2P communication scenarios we study. The algorithm can be implemented by utilizing only endtoend delay measurements between P2P nodes; hence, it can be readily deployed on today’s Internet. To support this claim, we have implemented the Primaldual algorithm for use in a peerassisted multiparty conferencing system and evaluated its performance through actual experiments on a LAN testbed and the Internet.
Random Linear Network Coding For Time Division Duplexing: When To Stop Talking And Start Listening
"... Abstract — We study the energy performance of random linear network coding for time division duplexing channels. We assume a packet erasure channel with nodes that cannot transmit and receive information simultaneously. The sender transmits coded data packets backtoback before stopping to wait for ..."
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Cited by 37 (16 self)
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Abstract — We study the energy performance of random linear network coding for time division duplexing channels. We assume a packet erasure channel with nodes that cannot transmit and receive information simultaneously. The sender transmits coded data packets backtoback before stopping to wait for the receiver to acknowledge the number of degrees of freedom, if any, that are required to decode correctly the information. Our analysis shows that, in terms of mean energy consumed, there is an optimal number of coded data packets to send before stopping to listen. This number depends on the energy needed to transmit each coded packet and the acknowledgment (ACK), probabilities of packet and ACK erasure, and the number of degrees of freedom that the receiver requires to decode the data. We show that its energy performance is superior to that of a fullduplex system. We also study the performance of our scheme when the number of coded packets is chosen to minimize the mean time to complete transmission as in [1]. Energy performance under this optimization criterion is found to be close to optimal, thus providing a good tradeoff between energy and time required to complete transmissions. I.
Energy efficient opportunistic network coding for wireless networks
, 2007
"... We consider energy efficient network coding design in wireless networks with multiple unicast sessions. Our approach decomposes multiple unicast sessions into a superposition of multicast and unicast sessions, with coding occurring only within each session. We give an optimization approach that is ..."
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Cited by 33 (0 self)
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We consider energy efficient network coding design in wireless networks with multiple unicast sessions. Our approach decomposes multiple unicast sessions into a superposition of multicast and unicast sessions, with coding occurring only within each session. We give an optimization approach that is more general than the existing poisonremedy optimization formulation. For the case of wireless, we consider XOR coding and give an achievable rate region for a primary interference model. To simplify network operation, we give an oblivious backpressure algorithm which does not optimize overhearing of transmissions, and a practical protocol called COPR based on the oblivious backpressure algorithm. Simulation experiments show that COPR largely reduces network power consumption over existing algorithms.
Crosslayer optimization for wireless multihop networks with pairwise intersession network coding
 IEEE Journal on Selected Areas in Communications
, 2009
"... Abstract—For wireless multihop networks with unicast sessions, most coding opportunities involve only two or three sessions as coding across many sessions requires greater transmission power to broadcast the coded symbol to many receivers, which enhances interference. This work shows that with a ne ..."
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Cited by 28 (2 self)
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Abstract—For wireless multihop networks with unicast sessions, most coding opportunities involve only two or three sessions as coding across many sessions requires greater transmission power to broadcast the coded symbol to many receivers, which enhances interference. This work shows that with a new flowbased characterization of pairwise intersession network coding (coding across two unicast sessions), an optimal joint coding, scheduling, and ratecontrol scheme can be devised and implemented using only the binary XOR operation. The new scheduling/ratecontrol scheme demonstrates provably graceful throughput degradation with imperfect scheduling, which facilitates the design tradeoff between the throughput optimality and computational complexity of different scheduling schemes. Our results show that pairwise intersession network coding improves the throughput of noncoding solutions regardless of whether perfect/imperfect scheduling is used. Both the deterministic and stochastic packet arrivals and departures are considered. This work shows a striking resemblance between pairwise intersession network coding and noncoded solutions, and thus advocates extensions of noncoding wisdoms to their network coding counterpart. Index Terms—Network coding, pairwise intersession network coding, imperfect scheduling, crosslayer optimization. I.
Dualities Between Entropy Functions and Network Codes
 IEEE transactions on information theory. 2008
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A Constant Bound on Throughput Improvement of Multicast Network Coding in Undirected Networks
, 2008
"... Recent research in network coding shows that, joint consideration of both coding and routing strategies may lead to higher information transmission rates than routing only. A fundamental question in the field of network coding is: how large can the throughput improvement due to network coding be? I ..."
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Cited by 21 (11 self)
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Recent research in network coding shows that, joint consideration of both coding and routing strategies may lead to higher information transmission rates than routing only. A fundamental question in the field of network coding is: how large can the throughput improvement due to network coding be? In this paper, we prove that in undirected networks, the ratio of achievable multicast throughput with network coding to that without network coding is bounded by a constant ratio of 2, i.e., network coding can at most double the throughput. This result holds for any undirected network topology, any link capacity configuration, any multicast group size, and any source information rate. This constant bound 2 represents the tightest bound that has been proved so far in general undirected settings, and is to be contrasted with the unbounded potential of network coding in improving multicast throughput in directed networks.
Network Tomography via Network Coding
 in Proc. of ITA Workshop , UCSD
, 2007
"... Abstract — In this work we show how existing network coding algorithms can be used to perform network tomography, i.e., estimate network topology. We first examine a simple variant of the popular distributed random network codes proposed by Ho et al. [14], and show how it can enable each network no ..."
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Cited by 18 (2 self)
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Abstract — In this work we show how existing network coding algorithms can be used to perform network tomography, i.e., estimate network topology. We first examine a simple variant of the popular distributed random network codes proposed by Ho et al. [14], and show how it can enable each network node to passively estimate the network topology upstream of it at no cost to throughput. The delays introduced by each upstream node and link can also be similarly estimated. We then consider the scenario wherein an adversary hidden in the network wishes to disrupt the estimation of network topology. We show how network errorcorrecting codes can be used to reliably perform network tomography if the network has sufficient connectivity, and demonstrate that network tomography is impossible otherwise. Index terms: Network coding, network tomography, topological identification, Byzantine adversaries. I.
Near Optimal Broadcast with Network Coding
 in Large Homogeneous Networks”, http://hal.inria.fr/inria00145231/en/, INRIA Research Report
, 2007
"... We study efficient broadcasting for wireless sensor networks, with network coding. We address this issue for homogeneous sensor networks in the plane. Our results are based on a simple principle (IREN/IRON), which sets the same rate on most of the nodes (wireless links) of the network. With this rat ..."
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Cited by 18 (10 self)
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We study efficient broadcasting for wireless sensor networks, with network coding. We address this issue for homogeneous sensor networks in the plane. Our results are based on a simple principle (IREN/IRON), which sets the same rate on most of the nodes (wireless links) of the network. With this rate selection, we give a value of the maximum achievable broadcast rate of the source: our central result is a proof of the value of the mincut for such networks, viewed as hypergraphs. Our metric for efficiency is the number of transmissions necessary to transmit one packet from the source to every destination: we show that IREN/IRON achieves near optimality for large networks; that is, asymptotically, nearly every transmission brings new information from the source to the receiver. As a consequence, network coding asymptotically outperforms any scheme that does not use network coding.