TELE3118 extras F or week 2

1. TELE3118 extras For week 2

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

3. modem Image from http://farm4.static.flickr.com/3290/3058587544_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 10110011100001001 101011 000111111 101011 0101000 101011 110001 101011 110100 101011 111110 101011 101011 101011 00000 Verifying message with check bits Red ≠ previously What values for check bits? 10110011100000000 101011 000111111 101011 0101000 101011 110000 101011 110110 101011 111010 101011 100010 101011 01001

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

8. Extra @ c7d9e2ec Hamming codes n-k check bits protect 2n-k-(n-k)-1 payload bits, e.g. 4 protect 11 All bits whose offset is a power of 2 (e.g. bit 1, 2, 4…) are check bits The value of check bit 2b-1 is chosen to ensure even parity over all bits whose position has a 1 in bit b, e.g. bit 1 (20) 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.: 0001 0010 0011 0100 0101 0110 0111 1000 1001 1010 1011 1100 1101 1110 1111 Bit #s and coverage of parity 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 e.g. payload of 11011110101 1 1 1 0 1 0 1 1 1 1 1 0 1 0 1 1 1 1 0 0 0 1 1 1 1 1 0 1 0 1 √ × Parity status √ × Parity status in binary 0 1 0 1 => error is in bit 5 Hamming codes are used in IEEE 802.16 Wireless networks