SHORT SEQUENCES AND CROSS-BIFIX ANALYSIS

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SHORT SEQUENCES AND CROSS-BIFIX ANALYSIS 

• Dragana Bajic, Cedomir Stefanovic

University of Novi Sad, Serbia and Montenegro
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PRESENTATION OUTLINE

• Introduction a mathematical problem
• Historical notes
• Application examples, so far
• ?

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HISTORICAL NOTES
Classical paper by Tolstrup Nielsen
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RANDOM START POSITION

• A STREAM OF RANDOM, EQUIPROBABLE DATA
• L alphabet (p 1/L)
• N pattern length

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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
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SEARCH FOR A SET OF Mgt1 SEQUENCES!
Pi0001 Pj0011
CROSS-BIFIX
Example P1000 P2001 P3100
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CROSS-BIFIX SPECTRUM
Triger ISITA2004
Tail vectors ri ri(0) ri(1) ri(N-1) ri(N)
h
Example P10001 P20011
Pr0q, Pr1p
r1 1 p pq pq2 pq3
r2 1 p p2 p2q p2q2
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STATISTICAL ANALYSIS
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STATISTICAL ANALYSIS
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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)

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SEARCH IN FRAME
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P.D.F. and PNS EXAMPLES
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SURVIVAL PROBABILITY
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SURVIVAL PROBABILITY
FOR SEQUENCES 0000 AND 0001 PNS 0!
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SURVIVAL PROBABILITY
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HÄBERLES CURVES

• N/F REDUNDANCY
• N MARKER LENGTH
• F FRAME LENGTH

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HÄBERLES CURVES e 1
P? 0!
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HÄBERLES CURVES E 1, Pegt0
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FURTHER APPLICATIONS

• Trigger from ICC2004 QPSK SEQUENCES (including
  distributed)
• Tricias 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.

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SHORT SEQUENCES AND CROSS-BIFIX ANALYSIS 

• THE END ?