1. TELE3118 extras For week 2

2. Slide from Ch. 3 of W. Stallings: Data and Computer Communications

3. 3 modem Image from http://farm4.static.flickr.com/3 290/3058587544_5afd150ed1 _o.jpg

4. Error checks

5. Decimal CRC 39592 3118 )123450000 -3*3118 29910 18480 28900 8280 2144 Add 3118-2144 = 974 Send 123450974

6. CRC example G=101011 10110011100000000 101011 000111111 101011 0101000 101011 110000 101011 110110 101011 111010 101011 100010 101011 01001 10110011100001001 101011 000111111 101011 0101000 101011 110001 101011 110100 101011 111110 101011 00000 What values for check bits? Verifying message with check bits Red ≠ previously

7. 10110001100001001 101011 000111011 101011 0100000 101011 101100-- 101011 111010 101011 100010 101011 10011 Detect an error in the data Detect a burst error

8. 8 Hamming codes n-k check bits protect 2 n-k -(n-k)-1 payload bits, e.g. 4 protect 11 2 All bits whose offset is a power of 2 (e.g. bit 1, 2, 4…) are check bits The value of check bit 2 b-1 is chosen to ensure even parity over all bits whose position has a 1 in bit b, e.g. bit 1 (2 0 ) covers odd bits If parity checks fail, and there is only one error, the number (“syndrome”) formed using digits reflecting parity outcome (0=OK, 1=fail) indicates the location of the error, e.g.: 111010111110101 123456789101112131415 e.g. payload of 11011110101 Bit #s and coverage of parity 111000111110101 √× ×√ 0101 => error is in bit 5 Parity status Parity status in binary Hamming codes are used in IEEE 802.16 Wireless networks 000100100011010001010110011110001001101010111100110111101111 Extra @ c7d9e2ec