Wireless Systems - Lecture. Network coding techniques. Elena Fasolo PhD Student - SIGNET Group firstname.lastname@example.org. March, 7 th 2004. Definition of network coding (NC).
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Network coding is a particular in-network data processing technique that exploits the characteristics of the wireless medium
(in particular, the broadcast communication channel)
in order to increase the capacity or the throughput of the network
The output flow at a given node is obtained as a linear combination of its input flows. The coefficients of the combination are, by definition, selected from a finite field
The content of any information flowing out of a set of non source nodes can be derived from the accumulated information that has flown into the set of nodes
 S.-Y. R. Li, R. W. Yeung, and N. Cai, “Linear network Coding”, IEEE Trans. on Information Theory, vol. 49, no. 2, Feb. 2003.
Source node of
Local encoding vector
Global encoding vector
If field size = 216 and |E| = 28 then Gtwill be invertible with probability ≥ 1−2−8 = 0.996
 R. Koetter,M.Medard, “An algebraic approach to network coding”, IEEE/ACM Trans. on Networking, Nov.2003
 P. A. Chou, T.Wu, and K. Jain, “Practical network coding”, in 51st Allerton Conf. Communication, Control and Computing, Oct. 2003.
All packets related to same source vectors x1,…, xhare said to be in the same generation; h is the generation size
All packets in same generation are tagged with same generation number (one byte - mod 256 - is sufficient)
Generations are useful to take into account the differences in data types, generation instants, priorities, etc.Generations
At source nodes
At the intermediated
aijObservations about the decoding phase
It can be decoded
h = 50 and field size = 28 overhead ≈ 50/1400 ≈ 3%
 J. Widmer, C. Fragouli, and J.-Y. L. Boudec, “Low–complexity energy–efficient broadcasting in wireless ad–hoc networks usign network coding”, in Proc.IEEE Information Theory Workshop, Oct. 2004.
 C. Fragouli, J. Widmer, and J.-Y. L. Boudec, “A network coding approach to energy efficient broadcasting”, Proceedings of INFOCOM06, April 2006.
All to all communication scenario
Energy consumption: number of transmissions and receptions needed to gather all the required packets
Delay: number of time units needed to decode all the required packets