1. ON THE INTERMEDIATE SYMBOL RECOVERY RATE OF RATELESS CODES Ali Talari, and Nazanin Rahnavard IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 60, NO. 5, MAY 2012 1

2. OUTLINE  Introduction  Related work  Rateless Code Design with High ISRR  RCSS: Rateless Code Symbol Sorting  Conclusion 2

3. INTRODUCTION  Design new rateless codes with close to optimal intermediate symbol recovery rates (ISRR) employing genetic algorithms.  Next, propose an algorithm to further improve the ISRR of the designed code, assuming an estimate of the channel erasure rate is available. 3

4. INTRODUCTION 4 Encoder S Decoder D Channel Limiteless Iteratively decoding z γ γ : intermediate range. Channel erasure rate

5. RELATED WORK 5 [4] S. Sanghavi, “Intermediate performance of rateless codes,” in Proc. 2007 IEEE Inf. Theory Workshop, pp. 478–482.

6. RELATED WORK  Employ feedbacks from D to keep S aware of z. [5][7]  Transmit output symbols in the order of their ascending degree. [6] 6 [5] A. Kamra, V. Misra, J. Feldman, and D. Rubenstein, “Growth codes: maximizing sensor network data persistence,” in Proc. 2006 Conf. Applications, Technologies, Architectures, Protocols Computer Commun., vol. 36, no. 4, pp. 255–266. [7] A. Beimel, S. Dolev, and N. Singer, “RT oblivious erasure correcting,” IEEE/ACM Trans. Netw., vol. 15, no. 6, pp. 1321–1332, 2007. [6] S. Kim and S. Lee, “Improved intermediate performance of rateless codes,” in Proc. 2009 Int. Conf. Advanced Commun. Technol., ICACT, vol. 3, pp. 1682– 1686.

7. RATELESS CODE DESIGN WITH HIGH ISRR 7

8. A. DECISION VARIABLES AND OBJECTIVE FUNCTIONS 8

9. A. DECISION VARIABLES AND OBJECTIVE FUNCTIONS (FOR ASYMPTOTIC CASE) 9

10. A. DECISION VARIABLES AND OBJECTIVE FUNCTIONS (FOR FINITE K) 10

11. B. OPTIMIZED RATELESS CODES FOR HIGH ISRR 11 [15] K. Deb, A. Pratap, S. Agarwal, and T. Meyarivan, “A fast and elitist multiobjective genetic algorithm: NSGA-II,” IEEE Trans. Evol. Comput., vol. 6, no. 2, pp. 182–197, Apr. 2002.

12. C. PERFORMANCE EVALUATION OF THE DESIGNED CODES 12

13. C. PERFORMANCE EVALUATION OF THE DESIGNED CODES 13 Summary: 1.Slightly differ from the distributions proposed in [4]. 2.The maximum degree is 19 from database observation. 3.As k decreases, large degrees are also eliminated.

14. C. PERFORMANCE EVALUATION OF THE DESIGNED CODES 14

15. C. PERFORMANCE EVALUATION OF THE DESIGNED CODES 15

16. RCSS: RATELESS CODED SYMBOL SORTING  The channel erasure rate ε may be available at S.  ε may be exploited as a side information to further improve the ISRR of rateless codes. 16

17. A. RCSS: RATELESS SYMBOL SORTING ALGORITHM 17

18. A. RCSS: RATELESS SYMBOL SORTING ALGORITHM 18

19. A. RCSS: RATELESS SYMBOL SORTING ALGORITHM 19 Input symbol Output symbol Initial() = 0 Action:

20. 20 A. RCSS: RATELESS SYMBOL SORTING ALGORITHM 20 Input symbol Output symbol

21. A. RCSS: RATELESS SYMBOL SORTING ALGORITHM 21

22. B. RCSS LOWER AND UPPER PERFORMANCE BOUNDS  Lemma 1: The performance of RCSS is upper bounded by z = γ for ε → 0.  Lemma 2: The performance of RCSS is lower bounded by the performance of [6] (where symbols are only sorted based on their degree) for ε → 1. 22

23. C. COMPLEXITY AND DELAY INCURRED BY RCSS 23

24. D. PERFORMANCE EVALUATION OF RCSS 24

25. E. EMPLOYING RCSS WITH CAPACITY- ACHIEVING CODES 25

26. 26

27. CONCLUSION  Design degree distributions that have optimal performance at all three selected points employing multi-objective genetic algorithms.  Proposed RCSS that exploits erasure rate ε and rearranges the transmission order of output symbols to further improve the ISRR of rateless codes. 27