1 / 21

Data communication line codes and constrained sequences

Data communication line codes and constrained sequences. A.J. Han Vinck May 18, 2003. A-synchronous arrivals: Line codes. Binary data transmitted using special signal form Important aspects: No DC content: average signal level = 0 High frequencies present in signal

wyanet
Download Presentation

Data communication line codes and constrained sequences

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 communicationline codes and constrained sequences A.J. Han Vinck May 18, 2003

  2. A-synchronous arrivals: Line codes • Binary data transmitted using special signal form • Important aspects: • No DC content: average signal level = 0 • High frequencies present in signal • Enough transitions in signal to gain timing information • Applications: • Optical transmission • Magnetic and Optical recording A.J. Han Vinck

  3. Line codes for clock recovery: examples 1 0 1 1 0 0 0 0 1 0 1 +5V 0 Basic frequency +5V 0 -5V Basic frequency factor of 2 higher! Longest run = 2 No DC Manchester code A.J. Han Vinck

  4. 4B/5B (FDDI) Property: 4 bits translated into 5 channel digits at most one „o“ at beginning; at most two „o“ at end Data code NRZI (change only when a „1“ occurs) 0000 11110 0001 01001 0010 10100 0011 10101 *** 1111 11100 Result: Longest run of „0s“ = 4 Longest run of „1s“ = 6 010001010 0101  01011 0110 01110 0111  01111 1000 10010 1001  10011 1010 10110 1011  10111 1100 11010 1101  11011 1110 11100 A.J. Han Vinck

  5. 4B/5B codes 1 0 1 1 0 0 0 0 1 0 1 DATA NRZI Rule NRZI: change only when a „1“ occurs A.J. Han Vinck

  6. Run Length Limited sequences (RLL) • maximum run of same symbols • changes in sequence used to synchronize • minimum run of same symbols • used to improve transmision efficiency Example: ( minimum = 2, maximum = 5 ) 00111000001111001100111 A.J. Han Vinck

  7. Ex:CD (EFM) uses min=2, max=10 Note: DvD uses EFM+ A.J. Han Vinck

  8. Problem: • Encoding into RLL sequence • Instead of RLL sequence consider (d,k)-constrained sequence • between 2 „ones“: maximum of k zeros; minimum of d zeros • The „ones“ indicate the position of a transition in the RLL sequence • ex: 0100010010001101  1000011100001001 Hence: RLL sequence has minimum run of d+1 and maximum of k+1 ex: the manchester code ( with efficiency ½ ) has (d,k) = (0,1) efficiency can be improved to 0.69! A.J. Han Vinck

  9. Why is it used in recording? no constraint: L bits take time  L/1 1 0 with constraint: L bits take time ‘ L/C(d,k), where C(d,k) < 1 1 0 same spacing: (d+1) units of time ‘= /(d+1) SURPRISE:‘L/C(d,k) =  L/[(d+1) C(d,k)] <  L for [(d+1) C(d,k)] > 1 A.J. Han Vinck

  10. Example: d = 1 00 00 or 11 2 d = 1 01 000 or 111 3 10 0000 or 1111 4 11 00000 or 11111 5 C(d,k) = 2/3.5 = 1/1.75 • With constraint L bits take ‘L/C(d,k) =  L/(d+1) C(d,k) = 0.875  L <  L SECRET: we changed the timing! A.J. Han Vinck

  11. Example (cont‘d) Example: 4 symbols 00,01,10,11 encode sequence 00, 01, 10, 00, 00... as 00, 111, 0000, 11, 00,..., where after every symbol we change polarity. The code is uniquely decodable! A.J. Han Vinck

  12. IBM disk code (d,k) = (2,7) (d,k) RLL • 10  1000 0000 or 1111 • 11  0100 0111 or 1000 • 011  000100 000111 or 111000 • 010  001000 001111 or 110000 • 000  100100 111000 or 000111 • 0011  00100100 00111000 or 11000111 • 0010  00001000 00001111 or 11110000 Homework: show that this code does not violate the constraint! A.J. Han Vinck

  13. Cont‘d Efficiency = ½ Maximum 0.51 (shown by Information theory) Instead of using L positions to store L bits of information we need only L/R*(d+1) = L/1.5 positions or 1/3 less! A.J. Han Vinck

  14. Eight to Fourteen Modulation (EFM) A.J. Han Vinck

  15. Efficient encoding example: d=1, k= • 000 00000 R = 3/5 = 0.6 (Maximum = 0.69) • 001 00001 • 010 00010 • 011 00100 R*(d+1) = 1.2 • 100 00101 • 101 01000 • 110 01001 • 111 01010 Problem: • What is maximum rate? • How to encode? A.J. Han Vinck

  16. Ex: Modified Frequency Modulation MFM (d,k) = (1,3) • Use markov state diagram to describe sequence generation 1/01 0/10 1/01 A 0/00 B Decoding rule: 0 x0 1 01 Efficiency = ½ Maximum = 0.55 • R*(d+1) = 1.0 A.J. Han Vinck

  17. Calculations of maximum rate C(d,k) C(d,k) := # of information bits/channel use • Use maximum entropy of the following Markov source • Information Theory gives the answer! Very important for practical applications: how far away from optimal? 0 0 0 0 0 0 1 2 d d+1 k 1 1 1 A.J. Han Vinck

  18. Shannons way out N(n) is the number of constrained sequences of lenght n The „capacity is then defined as A.J. Han Vinck

  19. Example (MFM) 0 0 0 S1 S2 S3 S4 1 1 1 # sequences in state S1 at time n = # sequences in state S1 at time n-2 + # sequences in state S1 at time n-3 + # sequences in state S1 at time n-4 A solution can be of the form: # sequences in state S1 at time n  cZn Then, we obtain the relation: Zn =Zn-2 +Zn-3 +Zn-4 A solution  for Z gives the rate as C = log2 (use previous formula) A.J. Han Vinck

  20. problem • For large d: exact timing detection of transition erroneous shift of transition is called peak shift (in recording) A.J. Han Vinck

  21. Other constrained codes Equal weight codes: # ones is the same for every code word example: 0011, 0101, 0110, 1001, 1010, 1100 DC-balanced: try to balance the number of ones and zeros example: transmit 000 or 111, 010 or 101 001 or 110, 100 or 011 only 1-bit redundancy, for every length Pulse Position modulation: weight 1 code words example: 001, 010, 100 A.J. Han Vinck

More Related