Abstract
D.Ing. (Electrical and Electronic)
In this thesis, the problem of undetected errors in digital communication systems
employing error detection as the only means of error control, is investigated. In the past,
the undetected error probability of linear block codes, was mainly investigated on the
binary symmetric channel, which is memoryless. With this thesis, the main aim was
to investigate the undetected error probability for linear block codes, on channels with
memory. The channel models investigated are the Gilbert-Elliott and Fritchman channel
models. Three techniques for calculating the undetected error probability on channels with
memory are investigated. These techniques are: (i) Exhaustive codeword generation, (ii)
Simulation and (iii) A trellis based technique. The trellis description of a block code
based on the states of a syndrome calculating linear feedback shift register, formed the
basis of the latter technique. The calculation of the weight spectrum of binary linear
block codes, is still largely an unsolved problem. Using the trellis description of a binary
linear block code, referred to earlier, we propose a description of binary linear block
codes based on graphs, and from this we develop a technique for calculating the weight
spectrum of binary linear block codes. The weight spectra of block codes determine the
undetected error probability of these codes when used on the binary symmetric channel.
Very favourable results were obtained through the application of the techniques developed
for undetected error probability calculation as well as weight spectrum calculation.