Publications related to Linear network coding

Delay with network coding and feedback

We consider the problem of minimizing delay when broadcasting over erasure channels with feedback. A sender wishes to communicate the same set of mu messages to several receivers over separate erasure channels. The sender can broadcast a single message or a combination (encoding) of messages at each timestep. Receivers provide feedback as to whether the transmission was received. If at some time step a receiver cannot identify a new message, delay is incurred. Our notion of delay is motivated by real-time applications that request progressively refined input, such as the successive refinement of an image encoded using multiple description coding. Our setup is novel because it combines coding techniques with feedback information to the end of minimizing delay. It allows Theta(mu) benefits as compared to previous approaches for offline algorithms, while feedback allows online algorithms to achieve smaller delay than online algorithms without feedback. Our main complexity results are that the offline minimization problem is NP-hard when the sender only schedules single messages and that the general problem remains NP-hard even when coding is allowed. However we show that coding does offer delay and complexity gains over scheduling. We also discuss online heuristics and evaluate their performance through simulations.

Ieee Service Center, 445 Hoes Lane, Po Box 1331, Piscataway, Nj 08855-1331 Usa2009

Online Broadcasting with Network Coding

Christina Fragouli, Lorenzo Keller

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 offline and online algorithms that optimize delay, both through theoretical analysis as well as simulation results.

2008

Delay with network coding and feedback

Christina Fragouli, Lorenzo Keller

We consider the problem of minimizing delay when broadcasting over erasure channels with feedback. A sender wishes to communicate the same set of μ messages to several receivers over separate erasure channels. The sender can broad- cast a single message or a combination (encoding) of messages at each timestep. Receivers provide feedback as to whether the transmission was received. If at some time step a receiver cannot identify a new message, delay is incurred. Our notion of delay is motivated by real-time applications that request progressively refined input, such as the successive refinement of an image encoded using multiple description coding. Our setup is novel because it combines coding techniques with feedback information to the end of minimizing delay. It allows Θ(μ) benefits as compared to previous approaches for offline algorithms, while feedback allows online algorithms to achieve smaller delay than online algorithms without feedback. Our main complexity results are that the offline minimization problem is NP-hard when the sender only schedules single messages and that the general problem remains N P -hard even when coding is allowed. However we show that coding does offer delay and complexity gains over scheduling. We also discuss online heuristics and evaluate their performance through simulations.

2009

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2013

Real-time Delay with Network Coding and Feedback

Christina Fragouli, Lorenzo Keller

We consider the problem of minimizing delay when broadcasting over erasure channels with feedback. A sender wishes to communicate the same set of m messages to several receivers. The sender can broadcast a single message or a combination (encoding) of messages to all receivers at each timestep, through separate erasure channels. Receivers provide feedback as to whether the transmission was received. If, at some time step, a receiver cannot identify a new message, delay is incurred. Our notion of delay is motivated by real-time applications that request progressively refined input, such as the refinements or different parts of an image. Our setup is novel because it combines coding techniques with feedback information to the end of minimizing delay. Uncoded scheduling or use of multiple description (MDS) codes has been well-studied in the literature. We show that our setup allows O( m ) benefits as compared to both previous approaches for offline algorithms, while feedback allows online algorithms to achieve smaller delay compared to online algorithms without feedback. Our main complexity results are that the offline minimization problem is NP-hard when the sender only schedules single messages and that the general problem remains NP-hard even when coding is allowed. However we show that coding does offer complexity gains by exhibiting specific classes of erasure instances that become trivial under coding schemes. We also discuss online heuristics and evaluate their performance through simulations.

2008

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In this paper, we give a characterization of the rate region for the degraded two message set problem, applied to a combination network with erasure channels. We also provide an algorithm that uses topological information in order to deliver the two messages to the receivers, and we show that our algorithm is optimal, in the sense that it achieves any rate pair in the region. We compare our algorithm analytically with a naive approach oblivious to the network structure, and we give an insight on what benefits should be expected for different classes of networks.

2010

Degraded multicasting with network coding over the combination network

Christina Fragouli, Shirin Saeedi Bidokhti

In this paper, we give a characterization of the rate region for the degraded two message set problem, applied to a combination network with erasure channels. We also provide an algorithm that uses topological information in order to deliver the two messages to the receivers, and we show that our algorithm is optimal, in the sense that it achieves any rate pair in the region. We compare our algorithm analytically with a naive approach oblivious to the network structure, and we give an insight on what benefits should be expected for different classes of networks.

2011

Building Wireless Network Coding Protocols

Lorenzo Keller

This work studies how to build wireless network protocols that achieve better reliability, lower delay and higher throughput than existing alternatives by using network coding and by exploiting the broadcast nature of the wireless channel. In the first part collection protocols, protocols used to gather information from a set of sources in a central location, are studied. Three scenaria where network coding helps data collection are discussed. First, network coding is used to reduce the overhead associated with end-to-end headers employed in traditional collection protocols. The main idea is to jointly code messages and identity of their sources using subspace codes. The benefits of the proposed protocol are assessed on a simulated testbed of wireless sensor nodes. Second, network coding is used to implement in-network function computation without requiring specialized operation of the routers. Finally, a complete protocol, SenseCode, is presented. This protocol uses network coding and overhearing as a lightweight alternative to multipath for improved reliability. The protocol performance is tested in a wide range of conditions using a simulated testbed of wireless nodes. The second part of the thesis shows how network coding can be used in broadcast protocols, protocols that are used to distribute information from a set of sources to all the network participants. First, flooding protocols for multi-hop networks are analyzed: the main objective is to improve reliability and reduce delay of this class of protocols. Existing codes and a novel scheme are tested using simulations and on a testbed made of mobile phones. Second, a complete system, MicroCast, that enables a group of mobile devices to receive high rate video content is presented. The system uses collaboratively the long range wireless links that connect each mobile device to the infrastructure and the short range local links that connect the devices among themselves. The system uses network coding and overhearing on the local links to improve the efficiency of utilization of the local radio resources.

EPFL2012

Information Flow Decomposition for Network Coding

Christina Fragouli, Emina Soljanin

The famous min-cut, max-flow theorem states that a source node can send a commodity through a network to a sink node at the rate determined by the flow of the min-cut separating the source and the sink. Recently it has been shown that by linear re-encoding at nodes in communications networks, the min-cut rate can be also achieved in multicasting to several sinks. Constructing such coding schemes efficiently is the subject of current research. The main idea in this paper is the identification of structural properties of multicast configurations, by decompositing the information flows into a minimal number of subtrees. This decomposition allows us to show that very different networks are equivalent from the coding point of view, and offers a method to identify such equivalence classes. It also allows us to divide the network coding problem into two almost independent problems: one of graph theory and the other of classical channel coding theory. This approach to network coding enables us to derive tight bounds on the network code alphabet size and calculate the throughput improvement network coding can offer for different configurations. But perhaps the most significant strength of our approach concerns future network coding practice. Namely, we propose algorithms to specify the coding operations at network nodes without the knowledge of the overall network topology. Such decentralized designs facilitate the construction of codes which can easily accommodate future changes in the network, e.g., addition of receivers and loss of links.

2006

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e analyze a special class of configurations with h sources and N receivers to demonstrate the throughput benefits of network coding and deterministic code design. We show that the throughput benefits network coding offers can increase proportionally to \sqrt{N}, with respect to the average as well as the minimum throughput. We also show that while for this class of configurations there exists a deterministic coding scheme that realizes these benefits using a binary alphabet, randomized coding may require an exponentially large alphabet size.

2005