1 / 27

On the Intermediate Symbol Recovery Rate of Rateless Codes

On the Intermediate Symbol Recovery Rate of Rateless Codes. Ali Talari, and Nazanin Rahnavard. IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 60, NO. 5, MAY 2012. outline. Introduction Related work Rateless Code Design with High ISRR RCSS: Rateless Code Symbol Sorting Conclusion.

decker
Download Presentation

On the Intermediate Symbol Recovery Rate of Rateless Codes

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. On the IntermediateSymbol Recovery Rate of Rateless Codes Ali Talari, and Nazanin Rahnavard IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 60, NO. 5, MAY 2012

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

  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.

  4. Introduction Encoder S Decoder D Channel encoded symbol Source symbol x={, ,.. } Iteratively decoding Limiteless

  5. Related work • The intermediate range of rateless codes can be divided into three regions.[4] • , , ) , , • designs optimal degree distributions, only optimal in one intermediate region. • k is infinite. [4] S. Sanghavi, “Intermediate performance of rateless codes,” in Proc. 2007 IEEE Inf. Theory Workshop, pp. 478–482.

  6. [7] A. Beimel, S. Dolev, and N. Singer, “RT oblivious erasure correcting,” IEEE/ACM Trans. Netw., vol. 15, no. 6, pp. 1321–1332, 2007. 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] [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. [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 • Design degree distributions for rateless coding with various k’s employing multi-objective genetic algorithms. • A. Tune the degree distribution Ω(.) considering all three intermediate regions of .

  8. A. Decision Variables and Objective Functions • Maximize , , and • conflicting objective functions, so • employ multi-objective optimization methods to design desired distributions. • A high ISRR have Ω(.)’s with much smaller maximum degree. • consider degree distributions with maximum degree of 50. • decision variables {,, . . . ,}, where .

  9. A. Decision Variables and Objective Functions (For asymptotic case) • : the probability that an input symbol is not recovered after l decoding iterations, where . • , and . • is convergent . • : the fixed point that is the final error rate of a rateless decoding with Ω(.) and γ. • hence,

  10. A. Decision Variables and Objective Functions (For finite k) • Find z for finite k we employ Monte-Carlo method by averaging z for a large enough number of decoding simulation experiments for . • , in this case, are found by numerical simulations.

  11. B. Optimized Rateless Codes for High ISRR • Employ NSGA-II multi-objective optimization algorithm[15] to find the distributions that have optimal z at three selected . • The results are available online at • http://cwnlab.ece.okstate.edu/research • four databases of degree distributions optimized for . [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 • A weighted function • From [4], • = 0.3934, • = 0.5828, • = 1 • We can find Ω(.) of interest by setting the appropriate weights and selecting the Ω(.) that minimizes F(Ω(.)). is the upper bound on z. is a tunable weight.

  13. C. Performance Evaluation of the Designed Codes • Summary: • Slightly differ from the distributions proposed in [4]. • The maximum degree is 19 from database observation. • As k decreases, large degrees are also eliminated.

  14. C. Performance Evaluation of the Designed Codes

  15. C. Performance Evaluation of the Designed Codes

  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.

  17. A. RCSS: Rateless Symbol Sorting Algorithm • Main idea: • choose an output symbol to be transmitted with that is the highest probability among the remaining output symbols. • =Pr( can recover an input symbol at D). • The decoder generate no feedback and RCSS can only employ the information available at source.

  18. A. RCSS: Rateless Symbol Sorting Algorithm • source S • generates output symbols, with erasure rate ε. • maintains a probability vector , = Pr( still not recovered at D). • N() is a set containing index of input symbols that are neighboring to . • () = Pr( can recover an input symbol at D.) • Assume () = 0, if has been previously transmitted.

  19. A. RCSS: Rateless Symbol Sorting Algorithm An output symbol can recover an input symbol iff all , have already been recovered. Initial() Input symbol Output symbol c1 N(1)={1,3} = 0 a1 a2 c2 N(2)={3} = 1- c3 N(3)={2,4} a3 = 0 c4 N(4)={1} = 1- a4 c5 N(5)={4,5} = 0 a5 c6 N(6)={5} = 1- transmit and update . Action:

  20. A. RCSS: Rateless Symbol Sorting Algorithm Input symbol Output symbol c1 N(1)={1,3} a1 a2 c2 N(2)={} c3 N(3)={2,4} a3 c4 N(4)={1} a4 c5 N(5)={4,5} a5 c6 N(6)={5} 20

  21. A. RCSS: Rateless Symbol Sorting Algorithm

  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.

  23. C. Complexity and Delay Incurred by RCSS • RCSS result in delays in transmission, since • all output sorted before transmission. • Eliminate the delay increases the memory requirements • Save an off-line version of . • Overall complexity

  24. D. Performance Evaluation of RCSS

  25. E. Employing RCSS With Capacity-Achieving Codes k = LT code parameters c = 0.05 = 0.01

  26. F. RCSS for Varying

  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.

More Related