Network Coding Theory

 Network Coding Theory Analysis Paper

Network Coding Theory

Raymond T. Yeung

Office of Information Anatomist The Chinese language University of Hong Kong

Training course Outline

Launch Linear Network Coding

1 . 2 . Acyclic Networks Cyclic Networks

Network Coding intended for Multiple Options Concluding Remarks

Introduction

Multicast vs Transmit

Broadcast

– One-to-many communication without specific receiver address

Multicast

– One-to-many interaction with particular receiver addresses

What is Network Coding?

The conventional approach (store-andforward) to multicasting is to you should find an efficient multicast tree inside the network, while using nodes acting as buttons which can path and/or repeat information. Network coding is a new theory which adjustments the way we believe of sending information in a network.

What is Network Coding?

In the paradigm of network coding, nodes can encode information received from the suggestions links before it is transmitted on the outcome links. Turning is a particular case of network coding.

A Network Coding Case

The Butterflies Network

b1 b1 b2

b2

b1 b1 b2

b2

b1

b1 b2

b2 b1

b2

b1

b1+b2 b1+b2 b1+b2

b2

A Network Coding Case with Two Sources

b1 b1 b2 b1 b2

b2 b2 b1 b1

b1 b1+b2 b1+b2

b2 b2

b1+b2

Wireless/Satellite Program

b1 b1 b2 b1+b2 b1+b2 b2

t=1

t=2

t=3

50% saving for downlink bandwidth!

Two Themes of Network Code

When there may be 1 supply to be multicast in a network, store-and-forward may possibly fail to optimize bandwidth. Once there are a couple of or more independent sources to become transmitted within a network (even for unicast), store-and-forward might fail to enhance bandwidth.

For what reason Surprising?

Time-honored information theory (C. Elizabeth. Shannon, 1948) tells us that for point-to-point communication, all information can in the end be represented as 3rd party (i. my spouse and i. d. ) bits through data compression. Independent bits cannot be further more compressed — commodity.

How come Surprising?

The folklore was that the product view for facts continues to apply in sites. For a long time, processing of information at the intermediate nodes in a network for the purpose of tranny has not been deemed.

Applications of Network Coding

Computer system Networks Wireless/Satellite Communications Allocated information storage/ dissemination (e. g., Bit-Torrent) Robust Network Management Network Error Modification

Recent Activities

Over a hundred and twenty papers have been written about them in the circumstance of – Information and Coding Theory – Network – Cellular Communications – Computer Science (algorithms, computational complexity) – Graph Theory, Matrix Theory

Recent Actions

Joint particular issue of IEEE Ventures on Details Theory and IEEE/ACM Ventures on Network Call for documents for numerous conferences (PODC 2004, ICC 2005, NetCod 2005/06, WirelessCom 2005, ISIT 2006, Intercontinental Symposium on Turbo Code 2006, etc) Tutorials by Globecom 2004, ISIT 2006.

Model of a Point-to-Point Network

A network is symbolized by a graph G = (V, E) with client set Sixth is v and border (channel) collection E. Emblematic from an alphabet N can be sent on each route. There can be multiple edges among a pair of nodes.

Single-Source Network Coding

The cause node S i9000 generates an information vector times = (x1 x2 … xω) ∈ Fω. Precisely what is the condition to get a node T to be able to get the information vector x?

Max-Flow Min-Cut Theorem

Consider a chart G = (V, E). There is a supply node S i9000 and a sink node T in set Versus. A cut in the graph G is actually a partition with the node collection V in two subsets V1 and V2 such that S is V1 and T is V2 The capacity of a lower is the amount of sides across the cut from V1 to V2

Max-Flow Min-Cut Theorem

The max-flow from S to T, denoted by maxflow(T), is the optimum rate where a liquid (e. g., water) can easily flow coming from S to T provided that the rate of flow in each border does not exceed 1 plus the flow conserves at each client. By the Max-Flow...


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