1 / 31

Data communication signatures

This document explores innovative optical transmission models, focusing on Pulse Position Modulation (PPM) and the significance of unique signatures in multi-access systems. It details the construction of prime codes from permutation codes, addressing their cardinality, orthogonality, and correlation properties. Key components such as optical orthogonal codes (OOCs) and Barker codes are analyzed for their effectiveness in achieving high peak-to-peak differences while minimizing cross-correlation. The implications of these codes on data recovery processes are also discussed, providing insights into advanced optical communication techniques.

xaviera-lagunas
Télécharger la présentation

Data communication signatures

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. Data communicationsignatures A.J. Han Vinck July 29, 2004

  2. Content:1. Optical transmission model2. Prime codes constructed from permutation codes 3. Optical Orthogonal Codes optical matched filter receiver auto- and cross correlation bound on cardinality4. Barker codes A.J. Han Vinck

  3. Optical transmisison model • Consider Pulse Position Modulation (PPM) with optical „ON-OFF“ keying • Users transmit M-ary signatures Example: M = 3 (sub)slots for a signature of length 3 3 2 1 A.J. Han Vinck

  4. Synchronous Communication model Transmit: 1:= signature; 0:= 0 sequence 1:= signature; 0:= 0 sequence Overlap with other users Detection: check presence of signature (yes or no) A.J. Han Vinck

  5. How does it work as multi-access system? - Each user is assigned a unique signature ( length -L-) the unique signature is multiplied by each bit (1 or 0) the signature is only known to the receiver in order to recover the data. - The most important part for correct recovery is the set of signatures A.J. Han Vinck

  6. Block Diagram Data Source # 1 Data Recovery Optical CDMA Encoder Optical CDMA Decoder Optical Star Coupler Data Recovery Data Source # N Optical CDMA Decoder Optical CDMA Encoder <----Transmitters-- <----Receivers-- A.J. Han Vinck

  7. Two optical orthogonal signatures with length L = 32 • First signature is represented by placing a pulse at the 1st, 10th 13th and 28th chip positions. • Second signature is represented by placing a pulse at the 1st, 5th 12th and 31st chip positions. Both signatures interfere in only one position A.J. Han Vinck

  8. Example: permutation code signatures:  length M M symbols (positions) are different  minimum # of differences dmin = M-1 i.e. maximum # of agreements = 1 Example: M = 3; M-1 = 2 Set of signatures: 123 312 231 132 321 213 A.J. Han Vinck

  9. Extension to M-ary Prime code construction: basis is permutation code with dmin = M-1 123 231 312 213 321 132 111 222 333 permutation code + extension Property:any two signatures agree in at most 1 position! check! A.J. Han Vinck

  10. Prime Code properties - # of agreements between any 2 signatures  1 Cardinality permutation code  M (M-1) + extension M - Cardinality PRIME code  M2 A.J. Han Vinck

  11. performance • In the no-noise, signature synchronous situation • We can accept M-1 other users, since the „interference“ is  1 A.J. Han Vinck

  12. Non-signature-synchronized User A # agreements = 2 (auto-correlation) User B # agreements = 2 (cross-correlation) A.J. Han Vinck

  13. signature Other users noise OPTICAL matched filter TRANSMITTER/RECEIVER A.J. Han Vinck

  14. What is the receiver doing? Collect all the ones in the signature: 0 0 0 1 0 1 1 delay 0 0 0 0 1 0 1 1 delay 2 0 0 0 1 0 1 1 delay 3 weight w A.J. Han Vinck

  15. We want: • weight w large high peak • side peaks  1 for other signatures cross correlation  1 A.J. Han Vinck

  16. „Optical“ Orthogonal Codes (OOC) • Property: x, y  {0, 1} AUTO CORRELATION CROSS CORRELATION x x y y cross shifted x x A.J. Han Vinck

  17. autocorrelation w = 3 0 0 0 1 0 1 1 signature x 0 0 0 1 0 1 1 0 0 0 1 0 1 1 1 1 1 3 1 1 1 side peak > 1 impossible auto correlation  2 Check! A.J. Han Vinck

  18. Sketch of proof B A 1 1 1 1 * 1 1 1 1 1 * 1 If * = 1, then interval A = B and auto correlation  2 A.J. Han Vinck

  19. Cross correlation 0 0 0 1 0 1 1signature x * * * 1 * * * signature y * * * 1 * * * * * * 1 * * ? Suppose that ? = 1 then cross correlation with x = 2 y contains same interval as x  impossible A.J. Han Vinck

  20. Intervals between ones ? 1,5 2,3 4,6 1 0 1 1 0 0 0 1 0 1 1 0 0 0 A.J. Han Vinck

  21. Important properties (for code construction) 1) All intervals  between two ones must be different 1000001  = 1, 6 1000010  = 2, 5 1000100  = 3, 4 C(7,2,1) 2) Cyclic shifts give cross correlation > 1 they are not in the OOC A.J. Han Vinck

  22. property 1: All intervals between ones are different, otherwise a shifted version of Y gives correlation 2 signature X 1 ------1---------1----1 signature Y 1---------11----1-----1 1 ------1---------1----1 1---------11----1-----1 A.J. Han Vinck

  23. property 2: Cyclic shifted versions are not good as signature X 1 ------1---------1----1 1 ------1---------1----1 X* --11 ------1---------1-- A shifted version of X* could give correlation 4 A.J. Han Vinck

  24. conclusion Signature in sync: peak of size w w must be large All other situations contributions  1 What about code parameters? A.J. Han Vinck

  25. Code size for code words of length n • # different intervals < n must be different otherwise correlation  2 • For weight w vector: w(w-1) intervals 1 1 0 1 0 0 0 1 1 0 1 0 00 |C(n,w,1)|  (n-1)/w(w-1) ( = 6/6 = 1) 1, 2, 3, 4, 5, 6 A.J. Han Vinck

  26. Sequences with „good“ correlation properties Example: count # of agreements - # of disagreements agreements: 1-1 AND 0-0 Barker 7 1 1 1 0 0 1 0 1 1 1 0 0 1 0 7 - 1 1 1 0 0 1 0 shift one position to the right - - 1 1 1 0 0 -1 - - - 1 1 1 0 0 - - - - 1 1 1 -1 - - - - - 1 1 0 - - - - - - 1 -1 A.J. Han Vinck

  27. Barker Codes examples Barker 11: [1,1,1,1,0,0,1,1,0,1,0] Barker 13: [1,1,1,1,1,0,0,1,1,0,1,0,1] The best we can do if „out of sync“: | # of agreements - # of disagreements |  1 Notes: Barker codes (Barker, 1950th) exist only for lengths: N = 2, 3, 4, 5, 7, 11, 13 IEEE 802.11 network uses the length 11- Barker code A.J. Han Vinck

  28. A.J. Han Vinck

  29. Application in 802.11b A.J. Han Vinck

  30. A.J. Han Vinck

  31. Application in Spread Spectrum A.J. Han Vinck

More Related