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SHORT SEQUENCES AND CROSS-BIFIX ANA LYSIS

SHORT SEQUENCES AND CROSS-BIFIX ANA LYSIS. Dragana Baji ć , Čedomir Stefanović. University of Novi Sad, Serbia and Montenegro. PRESENTATION OUTLINE. Introduction: a mathematical problem; Historical notes; Application examples, so far … ?. HISTORICAL NOTES.

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SHORT SEQUENCES AND CROSS-BIFIX ANA LYSIS

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  1. SHORT SEQUENCESANDCROSS-BIFIX ANALYSIS Dragana Bajić, Čedomir Stefanović University of Novi Sad, Serbia and Montenegro

  2. PRESENTATION OUTLINE Introduction: a mathematical problem; Historical notes; Application examples, so far … ?

  3. HISTORICAL NOTES Classical paper by Tolstrup Nielsen 1 2 3 4 5 6 7 8 RANDOM START POSITION • A STREAM OFRANDOM, EQUIPROBABLE DATA; • L – alphabet (p = 1/L); • N – pattern length

  4. 1 0 1 1 0 1 1 0 HISTORICAL NOTES BIFIX: both a prefix and a suffix! 1 0 1 1 0 1 1 0 h(2)= 1 DEFAULTS: h(0)= 1, h(N)= 1 h(5)= 1

  5. DEFAULT SEARCH FOR A SET OF M>1 SEQUENCES! Pi=0001 Pj=0011 CROSS-BIFIX Example: P1=000 P2=001 P3=100

  6. CROSS-BIFIX SPECTRUM: Triger: ISITA2004 Tail vectors: ri =[ri(0) ri(1) … ri(N-1) ri(N)] h: Example: P1=0001 P2=0011 Pr{0}=q, Pr{1}=p r1 = [1 ppqpq2pq3] r2 = [1 pp2p2qp2q2]

  7. STATISTICAL ANALYSIS

  8. STATISTICAL ANALYSIS

  9. APPLICATIONS SO FAR … Cross-bifix spectrum proves that Jones’ binary sequences (IEE) are indeed the best for alignment; Distributed sequences are the best in an error-free surrounding (Tricia); (Impossible sequences)

  10. SEARCH IN FRAME

  11. P.D.F. and PNS EXAMPLES

  12. SURVIVAL PROBABILITY

  13. SURVIVAL PROBABILITY FOR SEQUENCES 00…00 AND 00…01 PNS = 0!

  14. SURVIVAL PROBABILITY

  15. HÄBERLE’S CURVES • = N/F – REDUNDANCY N – MARKER LENGTH F – FRAME LENGTH

  16. HÄBERLE’S CURVES – e = 1 P = 0!

  17. HÄBERLE’S CURVES – E = 1, Pe>0

  18. FURTHER APPLICATIONS … Trigger from ICC2004: QPSK SEQUENCES (including distributed); Tricia’s idea: 3D acquisition curves for MIMO (not yet completely defined); Pilot-symbol assisted iterative carrier synchronization for burst transmission (ICC2004); Decoder-Assisted Frame Synchronization in the Presence of Phase/Frequency Noise (ICC2005); Search in non-equiprobable data (completely new approach to bifix and cross-bifix indicators)!!! HRV sequence analyzis, an approach similar to AppEn and SampEn.

  19. SHORT SEQUENCESANDCROSS-BIFIX ANALYSIS THE END ?

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