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

2. Ethernet Hub

3. Telephone Modem Standards 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

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

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

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

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

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

9. IP Checksum code

10. Addition: Multiplication: Division: x 3 + x + 1 ) x 6 + x 5 x 3 + x 2 + x x 6 + x 4 + x 3 x 5 + x 4 + x 3 x 5 + x 3 + x 2 x 4 + x 2 x 4 + x 2 + x x = q(x) quotient = r(x) remainder divisor dividend 35 ) 122 3 105 17 Polynomial Codes

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

12. Generator polynomial: g(x)= x 3 + x + 1 Information: (1,1,0,0) i(x) = x 3 + x 2 Encoding: x 3 i(x) = x 6 + x 5 1011 ) 1100000 1110 1011 1110 1011 1010 1011 010 x 3 + x + 1 ) x 6 + x 5 x 3 + x 2 + x x 6 + x 4 + x 3 x 5 + x 4 + x 3 x 5 + x 3 + x 2 x 4 + x 2 x 4 + x 2 + x x Transmitted codeword: b(x) = x 6 + x 5 + x b = (1,1,0,0,0,1,0) CRC Encoding example

13. reg 0reg 1reg 2 ++ Encoder for clockinputreg 0reg 1reg 2 0- 000 11=i 3 100 21=i 2 110 30=i 1 011 40=i 0 111 50101 60100 70010 check bits:r 0 = 0r 1 = 1r 2 = 0 r(x) = x Hardware implementation

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

15. 1. Single errors:e(x) = x i 0  i  n-1 If g(x) has more than one term, it cannot divide e(x) 2. Double errors: e(x) = x i + x j 0  i < j  n-1 = x i (1 + x j-i ) If g(x) is primitive, it will not divide (1 + x j-i ) for j-i  2 n-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) = x i 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 = 1/2 L-2 L > (n-k+1): fraction of bursts which are undetectable = 1/2 n-k L ith position error pattern d(x) Generator Polynomials (cont’d)

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

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

19. Asynchronous Data Transmission