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TELE3118 extras F or week 2

This slide presentation focuses on the fundamental concepts of error detection in data communications, specifically highlighting techniques such as Decimal CRC and Hamming codes. Topics covered include calculating check bits, detecting errors using syndromes, and ensuring data integrity through parity checks. The document provides practical examples to illustrate these methods, including calculations involving bit values and power of two offsets. Understanding these techniques is essential for maintaining reliable communication in networks, including IEEE 802.16 Wireless technologies.

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TELE3118 extras F or week 2

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  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

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