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