Abstract:

The influence of the theory of information on development of the error correcting coding theory has been studied. Main differences between the probabilistic approach and the deterministic approach in the analysis of error-correcting capabilities of different classes of linear codes have been demonstrated. The automaton hierarchical models for analysis of permutation decoding of cyclic codes have been developed and a cyclic permutation generator based on two Moore automata has been proposed. A study has been carried out into the regular and irregular states of linear finite-state machines (LFSM) based on the automaton representation of cyclic codes. A possibility of significant simplification of decoding of cyclic codes based on conversion of irregular LFSM syndromes into regular ones using permutations has been shown. The formalized methods for determination of error-correcting capabilities of iteratively decoded cyclic codes (IDCC) have been devised. They imply the replacementof traditional complete checking of all possible options for comparison of code words to directional search for the solution of the assigned problem, which leads to a significant time saving for calculations. The algorithm for determination of error-correcting capabilities of IDCC with respect to double errors is given. It has been shown that all iterative codes increase their error-correcting capabilities with an increase in the number of iterations and one can set it as a percentage for errors of various multiplicities. A distribution of error syndromes to separate iterations has been performed, which makes it possible to reduce the length of a check word in a code. As a result, this leads to an increase in a rate of iterative codes in comparison with the traditional correction codes.A comparative analysis of IDCC and LDPC codes has been carried out to determine a scope of their optimal use Author Biography Vasyl Semerenko, Vinnytsia National Technical University Khmelnytske highway, 95, Vinnytsia, Ukraine, 21021 PhD, Associate Professor Department of Computer Technique

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