1. Network Coding and Media Streaming (Invited Paper)
Nikolaos Thomos and Pascal Frossard
Signal Processing Laboratory (LTS4) Ecole Polytechnique F´ed´erale de Lausanne (EPFL), Lausanne, Switzerland JOURNAL OF COMMUNICATIONS, VOL. 4, NO. 9, OCTOBER 2009

2. Outline Introduction Network coding
Network coding in streaming application
Conclusion

3. Introduction This paper
describes the potentials of network coding in emerging delivery architectures such as overlay or peer-to-peer networks.
overviews the principles of practical network coding algorithms and outlines the challenges posed by multimedia streaming applications
provides a survey of the recent work on the application of network coding to media streaming applications

4. Network Coding
Network coding has recently emerged as an alternative to traditional routing algorithms in communication systems.
Pioneering work: [2] R. Ahlswede, N. Cai, S.-Y. R. Li, and R.W. Yeung, “Network information flow,” IEEE Trans. on Information Theory, vol. 46, no. 4, July 2000.
Improves the performance in data broadcasting
Most suitable setting: all to all communications

5. The Butterfly Network b1 b2 b1 b2 b1 b2 b1 b2 b1 b1+b2 b2 b2 b1 b1+b2S1 S2 S1 S2 b1 b2 b1 b2 b1 b2 b1 b2 b1
b1+b2 b2 b2 b1
b1+b2
b1+b2 C2 C2 C1 C1
(a) Traditional routing algorithm
(b) Network coding
The average throughput = 2 No transmission schedule.
The average throughput = 3/2 Need transmission schedule.

6. Wireless relay networks
1. Only 3 transmissions, and
2. reduce the energy consumption
of the antenna.

7. Error-prone tandem network
𝜀 𝑆1𝑅1
𝜀 𝑅1𝐶1
𝜀 𝑖𝑗 ：loss rate over the link ij.
𝜀 𝑆2𝑅1
S1 to C1
S1 to C1 R1 can encode and decode packet
Add S2 to network.
Communication rate
(1- 𝜀 𝑆1𝑅1 ) ∙ (1- 𝜀 𝑅1𝐶1 )
min{(1- 𝜀 𝑆1𝑅1 ) , (1- 𝜀 𝑅1𝐶1 )}
min{max{(1- 𝜀 𝑆1𝑅1 ) , (1- 𝜀 𝑆2𝑅1 )} , (1- 𝜀 𝑅1𝐶1 )}

8. Linear Network Coding
Linear network coding [21] is probably the most successful network coding algorithm due to its relatively low complexity and ability to achieve network capacity in multicast problems.
[21] S.-Y. R. Li, R. W. Yeung, and N. Cai, “Linear Network Coding,” IEEE Trans. Information Theory, vol. 49, no. 2, pp. 371–381, Feb

9. Linear Network Coding
When we refer to linear network coding [21], we intend that:
Coding can be implemented at low computational cost
Moreover, the information traversing a non source node has the following property:
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
[21] S.-Y. R. Li, R. W. Yeung, and N. Cai, “Linear Network Coding,” IEEE Trans. Information Theory, vol. 49, no. 2, pp. 371–381, Feb

10. Theoretical model for Linear NC
A directed, acyclic graph G(V,E) have unit-capacity edges.
Parallel edges are allowed.
A message is represented as 𝜔 symbols in a finite field F, and encoding/decoding is by means of linear operations in the finite field.

11. Local Description of Linear NC
Define the local encoding kernel of a 𝜔-dimensional network code at node t as a matrix of size 𝐼𝑛(𝑡)×𝑂𝑢𝑡(𝑡).
𝐾 𝑡 = [ 𝑘 𝑑,𝑒 ] 𝑑∈𝐼𝑛 𝑡 , 𝑒∈𝑂𝑢𝑡(𝑡)
𝐼𝑛(𝑡): the set of incoming links of node t.
𝑂𝑢𝑡(𝑡): the set of outgoing links of node t.
The local input-output relation at a node T is given by
𝑦 𝑒 = 𝑑∈𝐼𝑛(𝑇) 𝑘 𝑑,𝑒 ∙ 𝑦 𝑑 𝑦 𝑒 is the symbol sent on the channel e.
i.e., an output symbol from T is a linear combination of the input symbols at T.

12. Global Description of a Linear NC
The code maps the information vector x to each symbol 𝑦 𝑒 sent on the channel e.
𝑦 𝑒 =𝑥∙ 𝑓 𝑒
𝑓 𝑒 is called global encoding kernel.
The global description of linear NC
𝑓 𝑒 = 𝑑∈𝐼𝑛(𝑇) 𝑘 𝑑,𝑒 ∙ 𝑓 𝑑
The global description of a linear network code incorporates the local description.
𝑦 𝑒 =𝑥∙ 𝑓 𝑒 =𝑥∙ 𝑑∈𝐼𝑛 𝑇 𝑘 𝑑,𝑒 ∙ 𝑓 𝑑 = 𝑑∈𝐼𝑛 𝑇 𝑘 𝑑,𝑒 (𝑥∙ 𝑓 𝑑 ) = 𝑑∈𝐼𝑛 𝑇 𝑘 𝑑,𝑒 𝑦 𝑑 as in the local description.

13. Example of Linear NC

14. Desirable Properties of a Linear NC[10]
we have
dim( 𝑉 𝑇 )≤min⁡{𝜔,𝑚𝑎𝑥𝑓𝑙𝑜𝑤(𝑇)}.
An ω-dimensional F F-valued linear network code qualifies
as a
Linear multicast dim 𝑉 𝑡 = 𝜔 for every non source node t with
𝑚𝑎𝑥𝑓𝑙𝑜𝑤(𝑡)≥𝜔.
Linear broadcast dim 𝑉 𝑡 =min⁡{𝜔,𝑚𝑎𝑥𝑓𝑙𝑜𝑤(𝑡)} for every non
source node t.
Linear dispersion dim 𝑉 𝑇 =min⁡{𝜔,𝑚𝑎𝑥𝑓𝑙𝑜𝑤(𝑇)} for any set T
of non source nodes.
𝑉 𝑡 = < 𝑓 𝑑 :𝑑∈𝐼𝑛 𝑡 >
𝑉 𝑇 = 𝑡∈𝑇 𝑉 𝑡 ,
[10] R. W. Yeung, Information Theory and Network Coding, ser. Information Technology: Transmission, Processing and Storage. Springer-Verlag, 2008.

15. Linear Network Coding
The construction of a linear code has to consider both the value of 𝜔 and the network topology, along with the size of the base field F.
How to construct good linear network codes?
The global encoding kernels to be as independent as possible.
Select proper coefficients such that all local encoding kernels are full rank.
Several works have addressed the problem of the construction of good linear network codes.[23]-[29]

16. Practical Network Coding[18]
The problem of theoretical linear NC
Defining the coding coefficient uses computationally complex algorithm.
Servers have a full knowledge of network topology.
Linear NC is therefore not practical in large scale dynamic network.
Randomized Network Coding
The coefficient are randomly chosen in a sufficiently large Galois Field.
It permits to relax the requirements about the full knowledge of the network topology.
[18] P. A. Chou, Y. Wu, and K. Jain, “Practical Network Coding,” in Proc. of the 41st Allerton Conf. on Communication Control and Computing, Monticell, IL, USA, Oct

17. Practical Network Coding[18]
The author in [18] introduce the concept of generation.
In order to cope with the buffer delay problem.
A generation is a group of packets with similar decoding deadlines, which can be combined together by the network coding operations.
Trade-off
generation size(delay) v .s coding efficiency

18. Network coding in streaming application
The design of the system has to take the following specificities into consideration.
Strict delay constraints
High bandwidth requirement
Tolerance packet loss
Unequal importance of the data

19. Peer-to-Peer Streaming
The evaluation[36] shows that the network coding scheme is resilient to network dynamics.
[36] M. Wang and B. Li, “Lava: A Reality Check of Network
Coding in Peer-to-Peer Live Streaming,” in Proc. of IEEE
INFOCOM, Anchorage, Alaska, May 2007.

20. Peer-to-Peer Streaming
The organization of the peers in the overlay network has a large influence on the performance of the streaming system.
[39] K. Jain, L. Lovsz, and P. A. Chou, “Building Scalable and Robust Peer-to-Peer Overlay Networks for Broadcasting Using Network Coding,” Journal on Distributed Computing, vol. 19, no. 4, pp. 301–311, Dec
[40] J. Zhao, F. Yang, Q. Zhang, Z. Zhang, and F. Zhang, “LION: Layered Overlay Multicast With Network Coding,” IEEE Trans. Multimedia, vol. 8, no. 5, pp. 1021–1032, Oct
[41] Y. Liu, Y. Peng, W. Dou, and B. Guo, “Network Coding for Peer-to-Peer Live Media Streaming,” in Proc of the 5th Int. Conf. Grid and Cooperative Computing, Monticello, IL, USA, Oct. 2006, pp. 149–155.
[42] M. Shao, X. Wu, and N. Sarshar, “Rainbow Network Flow with Network Coding,” in Proc. of the 4th Workshop on Network Coding, Theory and Applications, NetCod, Hong Kong, China, Jan 2008, pp. 1–6.

21. Resiliency to Packet Losses
The media streaming system has to be robust to packet erasures and maintain low delay for improved performance.
Network-embedded FEC(NEF)[43],[44]
[43] S. Karande, M. Wu, and H. Radha, “Network Embedded FEC (NEF) for Video Multicast in Presence of Packet Loss Correlation,” in Proc. of IEEE Int. Conf. on Image Processing, vol. 1, Genoa, Italy, Sep. 2005, pp. 173–176.
[44] M. Wu, S. Karande, and H. Radha, “Network Embedded FEC for Optimum Throughput of Multicast Packet Video,” EURASIP Journal on Applied Signal Processing, vol. 20, no. 8, pp. 728–742, Sep

22. Prioritized Network Coding
Network coding based on Prioritized Encoding Transmission(PET)[34] can adapt to this property by handling the packets according to their priority.
[34] A. Albanese, J. Bloemer, J. Edmonds, M. Luby, and M. Sudan, “Priority Encoding Transmission,” IEEE Trans. Information Theory, vol. 42, pp. 1737–1744, Nov

23. Adaptively and Opportunistic Coding
When packet transmission can be overheard by multiple nodes, receivers could build up a buffer of packets that can be used to decode the successive packets.
The senders can thus use some knowledge about the receiver status to optimize network coding operations and reduce the overall transmission costs.
The COPE architecture has been presented in [58] for communication over wireless mesh networks.
[58] S. Katti, H. Rahui, W. Hu, D. Katabi, M. M´edard, and J. Crowcroft, “XORs in the air: practical wireless network coding,” in Proc of. ACM SIGCOMM, vol. 36, no. 4, New York, NY, USA, May 2006, pp. 243–254.

24. Adaptively and Opportunistic Coding[58]
[58] S. Katti, H. Rahui, W. Hu, D. Katabi, M. M´edard, and J. Crowcroft, “XORs in the air: practical wireless network coding,” in Proc of. ACM SIGCOMM, vol. 36, no. 4, New York, NY, USA, May 2006, pp. 243–254.

25. Conclusion
Network coding is an interesting paradigm that requests the network nodes to perform basic processing operations on packets in order to improve the throughput or the robustness of communication systems with network diversity.
There are still a few open issues to solve before network coding algorithms could be widely deployed in streaming applications.
Decoding complexity is pretty high in the most of the literature.
Distributed algorithms require to transmit coding information in the packet header, leading to overhead.
The choice of the right trade-off between delay, coding efficiency and complexity.