Linear network coding

Summary

In computer networking, linear network coding is a program in which intermediate nodes transmit data from source nodes to sink nodes by means of linear combinations. Linear network coding may be used to improve a network's throughput, efficiency, and scalability, as well as reducing attacks and eavesdropping. The nodes of a network take several packets and combine for transmission. This process may be used to attain the maximum possible information flow in a network. It has been proven that, theoretically, linear coding is enough to achieve the upper bound in multicast problems with one source. However linear coding is not sufficient in general; even for more general versions of linearity such as convolutional coding and filter-bank coding. Finding optimal coding solutions for general network problems with arbitrary demands is a hard problem, which can be NP-hard and even undecidable. Encoding and decoding In a linear network coding problem, a group of nodes P

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https://en.wikipedia.org/wiki/Linear_network_coding

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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 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

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