1 / 34

C oding is more than error correction A bit of magic

Inspired by Claude Shannon. C oding is more than error correction A bit of magic. A.J. Han Vinck. Coding is needed in high tech devices. fundamental limits set by Shannon (1948) . The Bell System Technical Journal, Vol. 27, pp. 379–423, 623–656, October , 1948. Bell Labs, 1955.

avi
Download Presentation

C oding is more than error correction A bit of magic

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. Inspired by Claude Shannon CodingismorethanerrorcorrectionA bitofmagic A.J. Han Vinck A.J. Han Vinck, Joburg September 2012

  2. A.J. Han Vinck, Joburg September 2012

  3. Codingisneeded in high techdevices A.J. Han Vinck, Joburg September 2012

  4. fundamental limitssetby Shannon (1948) The Bell System Technical Journal, Vol. 27, pp. 379–423, 623–656, October, 1948. Bell Labs, 1955. Fundamental problem: reproducingatthereceiver a messageselectedatthetransmitter Shannon‘scontribution: - bounds on theefficiency (capacity) - howtoachievethebounds A.J. Han Vinck, Joburg September 2012

  5. Introduction to the basic concepts message: Alpha codeword: (0 1 0 1 0 1 0 1) transmission error (0 0 0 1 0 1 0 1) decode (0 1 0 1 0 1 0 1) translate: Alpha How can we do that? A.J. Han Vinck, Joburg September 2012

  6. It works as follows • Use the difference in transmitted vectors to recover the transmitted original Example: 4 messages encoded as A 00 000 B 01 011 C 10 101 D  11 110 the words differ in at least 3 positions Hence, one difference (error) can be detected and corrected: receive: 10110 the transmitted message is? 11110 A.J. Han Vinck, Joburg September 2012

  7. 1-Error correctionstartedby Hamming (1950) 2 1 3 (3,1) (7,4) 123 000 111 (31,26) 3567 124 0000 000 1000 110 0100 101 ••• 1111 111 Every circlehasevenparity minimumdistancedmin= 3 info parities A.J. Han Vinck, Joburg September 2012

  8. Whataretheclassical research problems Codebook: maximize - # ofcodewordsoflength n - minimumdistancedmin • Channel characterization: • Types oferrors; memory in thenoisebehavior ? • Channel Capacity? • Decoder: • Design of a decoding/decisionalgorithm • Minimize complexity A.J. Han Vinck, Joburg September 2012

  9. Lecturecontent Goal:giveexamples, different from just errorcorrection - improvestorageefficiency in flashmemory - givebiometricsprivacy - code design for variable efficiency in networking - permutationcodesfor non-traditional errormodels A.J. Han Vinck, Joburg September 2012

  10. Ibm punch card „a flash memory“ Write, read and refresh Write, read and erase, but ••• Write, read and throw away, but ••• On the Capacity of Write-Unidirectional Memories with Nonperiodic Codes”, IEEE Transactions on Information theory, April 2004, pp. 649-656, (Fang-Wei Fu, A.J. Han Vinck, Victor Wei, Raymond Yeung) A.J. Han Vinck, Joburg September 2012

  11. A modern ROM: the Flash Memory Cell array in a flash memory A flash memory cell (Floating gate) • A flash memory cell stores charge / data • We can only increase the cell charge • If charge top level is reached, erase memory block A.J. Han Vinck, Joburg September 2012

  12. Writing in a q-ary flash memory cell Strategy for writing:increase charge content or stay at presentcontent Start at 0 cell charge level value bit Input 1, 0, 1, 0, 0, 0, 1, 1, 0, 1 1, 2, 3, 4, 4, 4, 5, 5, 6, 7 Cell Level 0 7 1 6 0 5 1 4 0 3 1 2 0 1 1 0 0 A.J. Han Vinck, Joburg September 2012

  13. Use thememory T=4 times: how many sequences we can write into the memory? q = 2: T+1 = 5 words write 0000 0011 0111 1111 0001 Note: writerandreader must knowthecontent! q = 3: 5 +T(T-1)/2 = 11 words write 0000 0011 0111 1111 0001 0012 0112 1112 0122 1122 1222 Capacity: log2|#sequences | ≈ (q-1) log2 (T+1) A.J. Han Vinck, Joburg September 2012

  14. Performance of the 1 step up strategy Probability (levelchange) = 2p(1-p) p probability P(1) = 1 – P(0) = p p 1-p p 1-p 1 0 1-p cell level 1 0 1 0 1 0 1 0 average number of writes to reach top level A.J. Han Vinck, Joburg September 2012

  15. Example of Codes: 2 bits in 3 cellsbefore erasing 00 01 10 11 2 bits 00 01 2 bits 10 11 A.J. Han Vinck, Joburg September 2012

  16. An artist‘s view of fingerprints A.J. Han Vinck, Joburg September 2012

  17. CodingforNoisyBiometricsusedas a key/password I am Han, can I come in? • - verifyclaimedidentitywithstoredinformation • problems: • Errors atauthentication: FalseRejection(FRR)/ FalseAcceptance(FAR) • Leakage: attackerfindsinformationaboutbiofrom Data Base (DB) A.J. Han Vinck, Joburg September 2012

  18. the Juels-Wattenberg scheme (binary) b‘(io) b(io) Random Codeword c c  b  b‘ = c  e c  b c  b c  b Enrollment Authentication Hash(c) = ? Data Base Hash(c) Y/N Hash(c) Ourcontributions: useknowledgeofbioatenrollmenttoencode use c  b fromdatabasetoimprovedecision on c Yanling Chen and Han Vinck, A fresh look into the biometric authentication: Perspective from Shannon’s secrecy system and a special wiretap channel, Secrypt, 2011 V. B. Balakirsky, A. R. G. and A. J. Han Vinck, Permutation block coding from biometrical authentication, Proc. 7th Int. Conf. on Computer Science and Info. Technologies, 2009 A.J. Han Vinck, Joburg September 2012

  19. Juels-Wattenberg for linear codes Secret s { 1,2,•••,2k } → RS codeword c = c1,c2,c3,••• ,cn c* b(io) changes t positions b => ---  --- ----- Enrollment:store c* SECURITY: 2t +1 > dmin Observer „cannot decode“ Authentication:b‘ points t positions in c* b‘ => ---  --- ----- due to „dust“ b‘ points at (t – e) incorrect and e correct positions (e errors in b‘) DECODABILITY: dmin – t > 2e WHY? Intuitive: Increasing dmin improves decodability, but decreases security and v.v. A.J. Han Vinck, Joburg September 2012

  20. Research topics we work on • Translation fromBioto Template • Iris, fingerprint, etc • Investigation oferrorbehavior • Burst, impulsive, non-linear • Performance estimationfor real data Practicalperformance FAR, FRR, etc. • Usingothertechniques, such asdatacompression • Fault tolerant hashing 011001… 000001… A.J. Han Vinck, Joburg September 2012

  21. Foundthisonesomewhere Escher A.J. Han Vinck, Joburg September 2012

  22. Communication over powerlines • Disturbances: • noise, attenuation, EMC, cable properties • Noise: • Narrowband noise • Impulsive noise (broadband) • Catastrophic effect on OFDM (multi-carrier) A.J. Han Vinck, Joburg September 2012

  23. A simple solution: Spread-FSK f0 f1 2-FSK mode Send: f0 or f1 : Detector: uses FSK or On-Off keying mode Advantages:robust against narrowband noise f f1 On-off mode f f0 alternative f1 Send: (f0,f1 ) or (f1,f0 ) i.e. R = 1/2 Detector: select max. # of agreements Advantages:robust against: narrowband + impulsive noise + random t f0 f1 t A.J. Han Vinck, Joburg September 2012

  24. effectofcorrectablenoise (simplified)here 2 x 2 f0 f0 f0 f1 f1 f1 t t t f0 f0 f1 f1 t t Redalwayshasthemajority! A.J. Han Vinck, Joburg September 2012

  25. General idea: representcodewordsas 2-dimensionalTime andfrequencypicture (123) (132) (231) t t t f f f (213) (321) (312) t t t f f f Minimum numberofdifferencesis TWO ! A.J. Han Vinck, Joburg September 2012

  26. effect of noise on permutation codes (simplified)here 3 x 3 t f Transmitted Background-insertion Background-deletion f Impulsive-broadband narrowband-jammer frequency selective fading A.J. Han Vinck, Joburg September 2012

  27. Research questions: • Design of code books: bounds on cardinality • Design of decoding algorithm: low complexity • Performance analysis: practical channels # of permutations price for distance „performance“ Hendrik C. Ferreira, A. J. Han Vinck, Theo G. Swart, Ian de Beer. Permutation trelliscodes. IEEE Transactions on Communications, 2005: 1782~1789 Constructing Coset Codes With Optimal Same-Symbol Weight for Detecting Narrowband Interference in M-FSK Systems IEEE Transactions on Information theory, December 2010, pp. 6347-6353 Versfeld, D. J. J.  Vinck, A. J. H.  Ridley, J. N.  Ferreira, H. C.  A.J. Han Vinck, Joburg September 2012

  28. Our (Olaf hooijenandme) modem design based on permutationcodes, 1997, Cebit Hannover A.J. Han Vinck, Joburg September 2012

  29. Piet Mondriaan Simple ideasneedcreativity (De Zuid-Afrikaanse gruwelprenten van Piet Mondriaan, wie kent ze nog?) A.J. Han Vinck, Joburg September 2012

  30. Some lessons I learned • Coding has a mathematical and a systems aspect • Applications are widespread: from networking to chip level • Implementations lead to low complexity algorithms • Viterbi (Convolutional Codes) • Berlekamp Massey (RS-codes) • Background knowledge in Information and Communication theory and combinatorics necessary • Cooperation with different disciplines important A.J. Han Vinck, Joburg September 2012

  31. Journal Papers with UJ-Wits-PCS scientists Constructing Coset Codes With Optimal Same-Symbol Weight for Detecting Narrowband Interference in M-FSK Systems IEEE Transactions on Information theory, December 2010, pp. 6347-6353 Versfeld, D. J. J. Vinck, A. J. H. Ridley, J. N. Ferreira, H. C. -„Combined Spectral Shaping Codes and OFDM Modulation for Narrowband Interference Channels,” K. Ouahada, H.C. Ferreira, A.J. Han Vinck, A.J. Snijders and T.G. Swart SAIEE Africa Research Journal, pp. 11-17, March 2008, ISSN 1991-169 - “Permutation Trellis Codes,” IEEE Tr. On Communications, pp. 1782-1789, November 2005, H.C. Ferreira, A.J. Han Vinck, T.G. Swart and I. de Beer. -“Power Line Communication”, Encyclopedia of Electrical and Electronics Engineering, Wiley, New York, Edited by John Webster, pp. 706-716, 199 H. Ferreira, H. Grove, O. Hooijen and A.J. Han Vinck, -“Insertion/Deletion Correction with Spectral Nulls” IEEE Trans. on Information Theory, March 1997, pp. 722-731. (H.C. Ferreira, W.A. Clarke, A. Helberg, K.A.S. Abdel-Ghaffarand A.J. Han Vinck) -"On the Undetected Error Probability of Linear Block Codes on Channels with Memory" IEEE Trans. on Information theory, Vol. 42, No. 1, January 1996, pp. 303-309. (A. Kuznetsov, F. Swarts, A.J. Han Vinck and H.C. Ferreira) -"A Class of DC-Free, Synchronization Error Correcting Codes" IEEE Trans. on Magnetics, Vol. MAG-29, No. 5, pp. 4048-4049, September 1993. (A.S.J. Helberg, W.A. Clarke, H.C. Ferreira and A.J. Han Vinck) A.J. Han Vinck, Joburg September 2012

  32. my scientific Genealogy (coincidence?)http://genealogy.math.ndsu.nodak.edu/ • Friedrich Leibnitz (1597, Leipzig) • Carl Friedrich Gauß (Göttingen) • John M. Wozencraft (MIT) (1925-2009) • Me (University Duisburg-Essen, Germany) • Digital Communications and - Codingtechniques A.J. Han Vinck, Joburg September 2012

  33. baie dankie! ngiyabonga ka khulu A.J. Han Vinck, Joburg September 2012

  34. EARLIEST DEPICTION OF JUGGLING knownshowsskillfulEgyptianwomen on the 15th Beni Hassan tombof an unknownprincefromtheMiddleKingdomperiodofabout 1994 to 1781 B.C Shannon jugglingmachineandjugglingtheorem A.J. Han Vinck, Joburg September 2012

More Related