Contents

1
Contents

• Communications Theory
• Parallel vs. serial transmission
• Transmission Capacity (Shannon)
• Error detection and correction
• Communications Media
• Optical fibers
• Coaxial cables
• Twisted pairs
• Wireless

2
Error Detection ExampleBelgian 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

3
Error detection and correction
k r lt LMax k bits r bits, f(inf.mess.) 2 k 2
kr
Length of messages Informative
message Redundancy Messages send
Messages received Hamming Distance (X-Y)
i1
????Xi-Yi
kr
4
Error detecting codes
k 1 r 1 red.bit inf.bit.
Hd 2
11
00
Single bit errors are detected if hamming
distance between legitimate messages gt 1. No
guessing is possible as erroneous messages are at
equal distances from several correct ones.
5
Error correcting codes
k 1 r 2 red.bits inf.bit.
Hd 3
111
000
Hamming distance between legitimate messages gt 2.
This implies that each erroneous message is
closer to one correct message than to any other.
6
Error correcting codes
Required Overhead for single bit error
correction kr lt 2r
information
redundancy
Overhead
1 lt 4 lt 11 lt 26 lt 57 lt 120 lt 247
2 3 4 5 6 7 8
200 75 36 19 11 6 3
7
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)