Bewertung von Codierverfahren für einen störungssicheren Datentransfer
The present thesis deals with modeling of unpredictable disturbances, called channel noise, which occur during the transfer of information over real transmission channels. A further main subject of the thesis is to develop an appropriate method for an evaluation of different coding techniques which are used to ensure a reliable data transfer. The development of this evaluation scheme is based on an appropriate channel model describing the unpredictable disturbances. In this thesis, the unpredictable disturbances which occur during the transmission of digital data are interpreted as a sequence of bit errors and are represented by a binary stochastic error process. To model the error process we use a Markovian background process with a finite state space and a transition matrix Q. By means of this approach we are able to model digital transmission channels with memory. Since within this approach the advantages of already known channel models are combined and their disadvantages are widely extenuated this basic approach provides some explicit advantages. To ensure a reliable transmission of information different coding techniques are used which follow different mathematical approaches and are characterized by their different algebraic properties. On the one hand there exist so-called "random error-correcting codes (REC)" which are more suited to correct randomly distributed transmission errors. On the other one there are so-called "burst error-correcting codes (BEC)" which are able to correct so-called burst errors, i.e. errors which are correlated. In this connection, the error-correcting capabilities of different codes depend on their different algebraic properties. Thus, a further objective of this thesis is to develop an appropriate method to compare and evaluate the efficiency of REC versus BEC. In general, as an appropriate measure for the success of an error-correcting code the residual error rate is being used. Based on the channel model proposed in the first part of the thesis we develop recursive equations to calculate the residual error rates of codes. In this context, we differentiate between REC and BEC; i.e. we consider the advantages of different mathematical approaches of different error-correcting codes in this evaluation of their performance. One important result is that the use of BEC should be preferred if the memory of the considered transmission channel is sufficiently strong. Another result is that by means of these recursive equations an optimal and adequate error-correcting code can be chosen a priori depending on the error statistics of the considered transmission channel.
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