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ELEN 602 Lecture 4

Review of last lecture Communication basics More on transmission media Errors in Transmission. ELEN 602 Lecture 4.      . Ethernet Hub. Usable frequency range of 500Hz to 2900 HZ W = 2400 HZ, signaling rate = 2400 pulses/second Use Trellis Modulation

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ELEN 602 Lecture 4

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  1. Review of last lecture Communication basics More on transmission media Errors in Transmission ELEN 602 Lecture 4

  2.       Ethernet Hub

  3. Usable frequency range of 500Hz to 2900 HZ W = 2400 HZ, signaling rate = 2400 pulses/second Use Trellis Modulation couples error detection capability into encoding For m bits of information, transmit (m+1) 2^(m+1) signaling levels, 2^m valid information In V.32bis standard 2400 pulses/sec, QAM 4, 4800 bits/sec 2400 pulses/sec, Trellis 32, 9600 bits/sec 2400 pulses/sec, Trellis 128, 14,000 bits/sec V.34bis standard - 2400, 4800, 9600, 14,400, 19,200, 28,800, 31,200, 33,600 bits/sec Telephone Modem Standards

  4. General Error Detection System All inputs to channel satisfy pattern/condition Channel output Deliver user information or set error alarm Pattern Checking User information Encoder Channel

  5. Error Detection Using Check bits Received information bits Information bits Recalculate check bits Channel Calculate check bits Compare Received check bits Check bits Information accepted if check bits match

  6. o o o o x x x o x o x o x x o o o o o o x x o o o o x x x o o o o o o x x o Code words A code with good distance properties (b) (a) A code with poor distance properties x = codewords o = non-codewords

  7. Two-Dimensional Parity check 1 0 0 1 0 0 0 1 0 0 0 1 1 0 0 1 0 0 1 1 0 1 1 0 1 0 0 1 1 1 Last column consists of check bits for each row Bottom row consists of check bit for each column

  8. Detectable and Undetectable Error patterns 1 0 0 1 0 0 0 0 0 0 0 1 1 0 0 1 0 0 1 1 0 1 1 0 1 0 0 1 1 1 1 0 0 1 0 0 0 0 0 0 0 1 1 0 0 1 0 0 1 0 0 1 1 0 1 0 0 1 1 1 One error Two errors 1 0 0 1 0 0 0 0 0 1 0 1 1 0 0 1 0 0 1 0 0 0 1 0 1 0 0 1 1 1 1 0 0 1 0 0 0 0 0 1 0 1 1 0 0 1 0 0 1 0 0 1 1 0 1 0 0 1 1 1 Four errors Three errors Arrows indicate failed check bits

  9. IP Checksum code

  10. Polynomial Codes Addition: Multiplication: = q(x) quotient x3 + x2 + x Division: x3 + x+ 1 ) x6 + x5 x6 + x4 + x3 dividend divisor x5 + x4 + x3 x5 + x3 + x2 3 35 ) 122 x4 + x2 105 x4 + x2 + x 17 x = r(x) remainder

  11. Steps: 1) Multiply i(x) by xn-k(puts zeros in (n-k) low order positions) 2) Divide xn-k i(x) by g(x) 3) Add remainder r(x) to xn-k i(x) (puts check bits in the n-k low order positions): Encoding Procedure quotient remainder xn-ki(x) = g(x) q(x) + r(x) transmitted codeword b(x) = xn-ki(x) + r(x)

  12. Generator polynomial: g(x)= x3 + x + 1 Information: (1,1,0,0) i(x) = x3 + x2 Encoding: x3i(x) = x6 + x5 CRC Encoding example x3 + x2 + x 1110 x3 + x+ 1 ) x6 + x5 1011 ) 1100000 x6 + x4 + x3 1011 x5 + x4 + x3 1110 1011 x5 + x3 + x2 1010 x4 + x2 1011 x4 + x2 + x x 010 • Transmitted codeword: • b(x) = x6 + x5 + x • b= (1,1,0,0,0,1,0)

  13. clock input reg 0 reg 1 reg 2 0 - 0 0 0 1 1=i3 1 0 0 2 1=i2 1 1 0 3 0=i1 0 1 1 4 0=i0 1 1 1 5 0 1 0 1 6 0 1 0 0 7 0 0 1 0 check bits: r0 = 0 r1 = 1 r2 = 0 Hardware implementation Encoder for reg 0 reg 1 reg 2 + + r(x) = x

  14. Additive Error model b(x) (Transmitter) R(x) (Receiver) + • e(x) Error pattern

  15. 1. Single errors: e(x) = xi0  in-1 If g(x) has more than one term, it cannot divide e(x) 2. Double errors:e(x) = xi+ xj0 i < jn-1 = xi(1 + xj-i) If g(x) is primitive, it will not divide (1 + xj-i) for j-i 2n-k1 3. Odd number of errors:e(1) =1 If number of errors is odd. If g(x) has (x+1) as a factor, then g(1) = 0 and all codewords have an even number of 1s. Generator Polynomials

  16. 4. Error bursts of length b: 0000110 • • • • 0001101100 • • • 0 e(x) = xi d(x) where deg(d(x)) = L-1 g(x) has degree n-k; g(x) cannot divide d(x) if deg(g(x))> deg(d(x)) L = (n-k) or less: all will be detected L = (n-k+1): deg(d(x)) = deg(g(x)) i.e. d(x) = g(x) is the only undetectable error pattern, fraction of bursts which are undetectable = 1/2L-2 L > (n-k+1): fraction of bursts which are undetectable = 1/2n-k Generator Polynomials (cont’d) ith position L error pattern d(x)

  17. (a) r Single bit input b (receiver) (transmitter) + e error pattern (b) Vector input r b (receiver) (transmitter) + e error pattern General Error Model

  18. RS-232 Serial line Interface 13 1 (a)                          14 25 (b) 1 Protective Ground (PGND) 1 2 Transmit Data (TXD) 2 Receive Data (RXD) 3 3 4 Request to Send (RTS) 4 Clear to Send (CTS) 5 5 DTE DCE 6 Data Set Ready (DSR) 6 Ground (G) 7 7 8 Carrier Detect (CD) 8 Data Terminal Ready (DTR) 20 20 22 Ring Indicator (RI) 22

  19. Asynchronous Data Transmission

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