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

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

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

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

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

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

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 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, [6] S. Kim and S. Lee, “Improved intermediate performance of rateless codes,” in Proc Int. Conf. Advanced Commun. Technol., ICACT, vol. 3, pp. 1682– 1686.

RATELESS CODE DESIGN WITH HIGH ISRR 7

A. DECISION VARIABLES AND OBJECTIVE FUNCTIONS 8

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

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

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

C. PERFORMANCE EVALUATION OF THE DESIGNED CODES 12

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.

C. PERFORMANCE EVALUATION OF THE DESIGNED CODES 14

C. PERFORMANCE EVALUATION OF THE DESIGNED CODES 15

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

A. RCSS: RATELESS SYMBOL SORTING ALGORITHM 17

A. RCSS: RATELESS SYMBOL SORTING ALGORITHM 18

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

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

A. RCSS: RATELESS SYMBOL SORTING ALGORITHM 21

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

C. COMPLEXITY AND DELAY INCURRED BY RCSS 23

D. PERFORMANCE EVALUATION OF RCSS 24

E. EMPLOYING RCSS WITH CAPACITY- ACHIEVING CODES 25

26

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