Dec 15, 2006 - Suppose n original packets (before encoded) are M1,M2,â¦, Mn. ⢠Each encoded packet X = â i=1:n g i. Mi. ⢠Here g i is coefficients belonging ...
Network Coding: An Instant Primer Wu Xiaobing GPS Group@NJUCS Dec. 15, 2006
Paper Information • Title: Network Coding: An Instant Primer • Authors: C. Fragouli, J. –Y. Le Boudec, and J. Widmer, EPFL. • Publication: ACM SIGCOMM Computer Communication Review 2006.
Outline • • • • •
Introduction What’s NC? Benefits of NC Application of NC Conclusion
Introduction • Traditional a
a b
• With NC
b
a
a⊕b
a⊕b
b
Assumption behind traditional network traffic • Information is separate, although it may share network resources. (say, cars in highways.) • NC breaks this assumption!
What’s NC? • A technology to combine several data packets into one or several output packets.
Linear NC • NC is commonly referred to as Linear Network Coding. • XOR is replaced by linear operations, i.e., addition and multiplication. • 2x + 10y-3z is a linear combination of (x,y,z).
Linear NC (cont’d) • Suppose the length of each packet is L bits. (Add zeros if it is less than L.) S bits
L bits
• Each packet can be viewed as a vector with L/S elements.
Linear NC (cont’d) • Each element belongs to [0, 2s-1]. • All linear operations are performed over the field F{2s}. F{2s} refers to [0, 2s-1]. • After linear combinations, the resulted packet still has a length of L.
LNC-Encoding • Suppose n original packets (before encoded) are M1,M2,…, Mn. • Each encoded packet X = ∑i=1:ngiMi. • Here gi is coefficients belonging to F{2s}.
LNC-Encoding (cont’d) • Actually, the summation is perform for each “element” of the packet. • Xk = ∑i=1:ngiMik, 1
domain, can begin to reap the benefits of network coding with the development of a ... hitless1 tail-end switching scheme, the node in the middle would repeat, in two separate ... and receiver) that we obtain with network coding, but at a cost.
Thm: One network code works for all feasible link failures. ⢠Proof: Treat each set of link failures as a different destination in a multicast network. ⢠Interior nodes ...
received from the input links before it is transmitted on the ..... âThe local input-output relation at a node T is given by ..... Complexity Analysis. â Recall that N ...
Concepts. Motivation. The feasibility conditions in the previous part requires the knowledge of entire network topology. Information Theory and Coding Seminars ...
Apr 3, 2006 - multiple destinations, it sends one copy of the data packets onto each output link ..... to the size for a mobile handset or renders a colored image in black .... linear network code when the base field F is sufficiently large. Theo-.
pairwise intersession network coding, a joint optimal scheduling ..... identical. The impact of PINC on rate-control and scheduling is thus minimal and confined ...
Apr 3, 2006 - 101. 7. Output the index of ucd in Tn. [Ucd]δ as the codeword and send ...... of Technology, Department of Electrical Engineering and Computer ...
Jan 21, 2005 - ... a theoretical point of view, this is a very attractive interdisciplinary study area that poses interesting questions .... This is not a problem for nonreal-time applications (e.g. file transfer), ... http://personal.ie.cuhk.edu.hk/
the idea for which was first proposed by Ahlswede et al. in ... idea was originally meant for wired networks with special ..... Though the work is in progress and.
AbstractâRecently, there has been a lot of discussions on Avalanche, a Microsoft prototype for large scale content distribution on a peer-to- peer network that ...
The anmunt of information that can he sent with- out network coding is ... ternlinals (mo,. . . :mh]. The Steiner packing number is given by the following linear.
rate of a subcarrier depends not only on its fading profile, but also on which link it ... MS using the training sequence in OFDMA systems [7], and then signaled to ...
Pt-to-Pt. Transfer. Matrices. Multicast. General. Conclusion. An Example. Recall that in a linear network the random process on an edge is given by. Y (e) = µ(v).
problem that we call the Hybrid strategy: one special storage node maintains one full ..... [1] A. G. Dimakis, P. G. Godfrey, M. J. Wainwright, and K. Ramchan-.
However, multicast on overlay networks does not perform as well as IP .... Rodriguez [12] explored application of network coding to unstructured overlay ...
A directed graph is said to be cyclic if it contains a directed cycle, i.e., there exists a .... 1) The symbols transmitted over the network belong to a (sufficiently large) ...
Jun 2, 2009 - {joaovilela, luisalima, barros}@dcc.fc.up.pt ... preventing intermediate nodes from running their standard net- work coding operations. ... Canonical network coding example: node 1 multicasts bits a and b to nodes 6 and 7.
Jun 2, 2009 - several upstream nodes concurrently with random network coding, by ... chooses a set of coding coefficients [c1,c2, ··· ,cn] in the. Galois field ...
Jun 11, 2009 - The use of hybrid methods that exploit both the benefits of channel coding and ... [5] A. G. Dimakis, P. B. Godfrey, M. J. Wainwright, and K.
multicast in the application-layer, by using overlay networks (e.g., [1], [2], [3], [4], [5]). The general ... Section III gives overview of previous research on network coding, ... operations are defined as linear combinations over finite fields wit
(we make precise later the meaning of linear codes, since the codes are not bit-wise ...... routing may be optimal or near-optimal for achieving network capacity.
multiple upstream peers is a typical way of achieving high throughput .... segment i until it has received m linear independent blocks. [c1 i,c2 i,...,cm i]. To decode ...
which needs four time slots to complete a cycle of information exchange ...... when µ is very small; it approaches unity for the ONC scheme ... shop, Sep. 2007.
1-4244-0222-0/06/$20.00 (c)2006 IEEE. Authorized ... we can find exact results) and on random, realistic networks. (where we obtain ... We are interested in calculating. Tnc. Tw ... placed at equal distances around a circle as depicted in Fig. 1.