New Degree Distribution to improve LT-Code in Network Coding for Broadcasting in Ad-hoc Wireless Networks

1. New Degree Distribution to improve LT-Code in Network Coding for Broadcasting in Ad-hoc Wireless Networks Nour KADI, Khaldoun Al AGHA 21st Annual IEEE International Symposium on Personal, Indoor and Mobile Radio Communications

2. Outline • Introduction • Previous work • The drawback of LT codes • Switched Code • Analysis of Switched Distribution • Simulation • Conclusions

3. Introduction(1/3) - ad-hoc network • A wireless ad hoc network is a decentralized type of wireless network. • wireless Sensor networks (WSN) • Eachnode participates in routing by forwarding data for other nodes, and so the determination of which nodes forward data is made dynamically based on the network connectivity. 

4. Introduction(2/3) • Overcoming problems associated with resource scarcity and unreliable channels has been a challenge for data broadcasting protocols in ad-hoc networks. • The network coding combined with network broadcasting can reduce the bandwidth and power consumption and increase the throughput. • Rateless codes achieve a reliable broadcast transmission.

5. Network Coding b1 b2 b1 b2 b1 b2 b2 b1 b2 b1

6. The number of transmissions(1/2) (for channel coding)

7. The number of transmissions(2/2) (For network coding)

8. [4]D. S. Lun, M. M´edard, R. Koetter, and M. Effros, “On coding for reliable communication over packet networks,” CoRR, vol. abs/cs/0510070, 2005. Previous work

9. Introduction(3/3) • To achieve reliable broadcasting and efficient bandwidth utilization： • Using LT-code guarantees the simple complexity of the proposed coding scheme. • Using network coding increases the throughput and saves the network resources. • We introduce a coding scheme that efficiently broadcasts the source packets.

10. Switched Code(1/2) • Combines LT-code with network coding, by enabling intermediate nodes to perform coding.

11. The drawback of the LT codes • The RSDis designed to decode plenty of symbols only when it receives sufficiently large number of encoded packets. • Hence, using LT- code in its original form increases significantly the end-to-end packet delay.

12. Switched Code(2/2) • We present a degree distribution that increases the symbol recovery probability at any time during the decoding process, while keeping the overhead as small as possible.

13. Switched distribution • The sender switches from the first distribution to the other according to the number of encoded packets which have been sent. [6] S. Agarwal, A. Hagedorn, and A. Trachtenberg, “Adaptive rateless coding under partial information,” in Information Theory and Applications Workshop, 2008, 2008, pp. 5–11.

14. Degree distribution of LT codes

15. Analysis of Switched Distribution(1/8) Definition 1.(codeword and degree): 2 4 3 5 1 Codeword with coding candidate {1, 3, 4}, and degree = 3 Definition 2.Binary Exponential Distribution():

16. Analysis of Switched Distribution(2/8) • Definition 3. (The Decoding Probability): Let be the probability to decode a codeword of degree d when r − 1 of the source symbols has been recovered.

17. Analysis of Switched Distribution(3/8) • Definition 4.(The Symbol Recovery Probability): Let be the probability to recover the source symbol. So , where p(d) is the probability to have a codeword of degree d. • Definition 5. Let be The expected number of recovered symbols after sending y codewords. And let the overhead = Y − k where = k. In addition to minimize the overhead, our interest is to maximize , This could be obtained by maximizing , r.

18. Analysis of Switched Distribution(4/8) • Lemma 2. To recover the first symbol at the destination, it is more useful that the source chooses the degree of the codeword according to Binary Exponential Distribution than using Robust Soliton Distribution (RSD). Because (i) () (ii) , where , and ( H()+), H(n) is the Harmonic number of n. (RSD) We can prove that .

19. Analysis of Switched Distribution(5/8) • Lemma 3. To recover the last symbol, it is more useful to use Soliton Distribution. In this case r=k, from proposition 1, (BED) (Ideal Soliton distribution) And we can prove that .

20. Analysis of Switched Distribution(6/8) • Lemma 4. RSD outperforms only after recovering 70% of the source packets at the destination. Using a dichotomic technique, we find that when r − 1 is inferior to 0.70*k then is superior to and this is reversed when r − 1 becomes superior to 0.70*k.

21. Analysis of Switched Distribution(7/8) • Definition 6.Let’s consider an incremental decoder S. If the decoder S receives r codewords, then it decodes them in an ascending order according to their degree d. First step, it decodes the packets with d = 1. Then, using the packets which are recovered from the first step, it decodes the packets with d = 2 . For a step i, it decodes the packets with d = i by using the packets which are recovered from steps 1,2,. . . ,i-1. If a packet of degree d couldn’t be decoded at step i = d, then it will be ignored in the next steps.

22. Analysis of Switched Distribution(8/8) • Proposition 2. The expected number of recovered symbols after sending k codewords according to is at least 0.70*k. Prove this proposition for the incremental decoder. Assume that S receives Y codewords, then Step 1：= Step 2： =

23. Then, the total expected number of recovered symbols is Using a dichotomic technique, we find that when Y=k then =0.70*k. And this result is valid for a non-restricted decoder.

24. Shifted Robust Soliton Distribution SRSD[6] • To adapt LT code to the case where some input symbols are already known at the destination. • Generate high degree with higher probability k : total number of input symbols l : the number of input symbols already known at the destination.

25. Simulation(1/2) • Using Opnet simulator • The simulation continues until k source packets generated by the source node are delivered to all other nodes. • At each time slot, an intermediate node can transmit one packet, which is received by its neighbors with a probability (1-). • Using distributed TDMA scheduling • Running the simulation 30 times • The parameters of RSD • C=0.2,

26. [4] P. Pakzad, C. Fragouli, and A. Shokrollahi, “Coding schemes for line networks,” CoRR, vol. abs/cs/0508124, 2005. Simulation(2/2) • Comparison with 2 other LT-code based schemes. • Original LT code • Forward & Re-code[4] (for line network) • Adapt LT-code with RSD to network coding • Comparison with a random linear network coding schemes. • Probabilistic NC[8] • Random linear network coding with a probabilistic approach [8] C. Fragouli, J. Widmer, and J.-Y. L. Boudec, “Efficient broadcasting using network coding,” IEEE/ACM Trans. Netw, vol. 16, no. 2, pp. 450–463, 2008.

27. Compare with LT-code based schemes(1/2) loss rate 30 static node in line network

28. Comparison with LT-code based schemes(2/2) 30 static node in line network , k=10 The deliver ratio is the number of delivered packets at the destination over the total number of the source packets.

29. Comparison with a random linear network coding schemes 50 nodes placed randomly on a area.

30. Conclusions • Considered the broadcast traffic in ad-hoc wireless networks, We have presented a novel rateless code which outperforms LT code as it allows intermediate nodes to process the received packets. • The proposed distribution increases the decoding probability of any received symbol. • The simulation shows that our scheme reduces the number of transmissions and increases the packet delivery ratio.