1. Error control coding for wireless communication technologies
Background material for Hamming codes
EU-USA Atlantis Programme
FIT & Budapest University of Technology and Economics

2. Objective Design a code which can correct every single error.
Motivation:
If the channel is good then it is enough to have a limited error correcting capability.

3. Probability distribution of the weight of the error vector
BSC with n 5 6 7
P(w(e)>1)
0,00001
0,000014
0,00002

4. Error detection with matching gates
syndrome vector s 1 1 1
Identified error vector e 1

5. Error detection with matching gates (operation)1 1
e=(010) 1 1 1

6. Error detection with matching gates (operation)1 1 1
e=(100) 1 1

7. Error detection with matching gates (operation)1 1
e=(001) 1 1 1

8. The full coding scheme 1 1 1 G H 1 Tr 1

9. Suggested readings
D. Costello: Error control codes, Wiley, 2005, Chapter 3

10. Expected Quiz question
Given a generator matrix of a linear binary systematic code, determine the error group belonging to a given error vector
Give the parity check matrix of the C(15,11) Hamming code

11. Thank you for your attention !