Contents Communications Theory Parallel vs serial transmission Transmission

Contents • Communications Theory – Parallel vs. serial transmission – Transmission Capacity (Shannon) – Error detection and correction • Communications Media – Optical fibers – Coaxial cables – Twisted pairs – Wireless Postacademic Interuniversity Course in Information Technology – Module C 1 p 1

Error Detection Example Belgian Bank Account Numbers • Bank account number structure – Bank identification : 3 digits – Account number : 7 digits – Error detection : 2 digits • The ten first digits modulo 97 are appended for error detection purposes. • This algorithm allows detection of all single digit errors • Example : – 140 -0571659 -08. 1400571659 MOD 97 = 08 – 140 -0671659 -08. 1400671659 MOD 97 = 01 Postacademic Interuniversity Course in Information Technology – Module C 1 p 2

Error detection and correction Length of messages : k + r <= LMax Informative message: k bits Redundancy: r bits, f(inf. mess. ) # Messages send: 2 k # Messages received: 2 k+r i=1 |Xi-Yi| Hamming Distance (X-Y): k+r Postacademic Interuniversity Course in Information Technology – Module C 1 p 3

Error detecting codes k = 1; red. bit = inf. bit. 01 11 00 00 Hd = 2 11 10 Single bit errors are detected if hamming distance between legitimate messages > 1. No guessing is possible as erroneous messages are at equal distances from several correct ones. Postacademic Interuniversity Course in Information Technology – Module C 1 p 4

Error correcting codes k = 1; r = 2; red. bits = inf. bit. 011 010 111 110 001 000 Hd = 3 111 100 Hamming distance between legitimate messages > 2. This implies that each erroneous message is closer to one correct message than to any other. Postacademic Interuniversity Course in Information Technology – Module C 1 p 5

Error correcting codes Required Overhead for single bit error correction k+r < 2 r information redundancy Overhead 1 <= 4 <= 11 <= 26 <= 57 <= 120 <= 247 2 3 4 5 6 7 8 200 % 75 % 36 % 19 % 11 % 6% 3% Postacademic Interuniversity Course in Information Technology – Module C 1 p 6

Error Correction • Error detecting codes – Correction by retransmission of erroneous blocks – If few errors, very low overhead – Most common approach to error correction in data communications • Error correcting codes – Very high overhead with short data blocks – Longer data blocks can have multiple errors – Used when retransmission impossible or impractical – Also used when error rate rather high. – Error correcting codes for long blocks, with multiple errors exist and are used (trellis encoding) Postacademic Interuniversity Course in Information Technology – Module C 1 p 7