IMPROVEMENT OF CYCLIC CODES EFFECTIVENESS BY COMBINATORIAL OPTIMIZATION METHODS

Abstract

The methods of improving the cyclic codes efficiency constructed on the basis of combinatorial configurations of the type "ideal ring bundles" (IRB) s by three factors – correction ability, power of coding method and complexity of the decoding procedure are considered. The method is based on the principle of combinatorial optimization, grounded on the algebraic theory of ordered integer sequences with a circular structure, all the numbers, as well as all sums of consecutive numbers exhaust the value sofnatural row numbers. Two theoretically grounded approaches to increase of noise immunity of cyclic codes are offered: implementation of optimized IRB-code, as well as monolithic and group one. Optimized cyclic IRB-code favorably differs from the rest of the codes of this class by the highest correction capacity at the same length of code words. Optimized IRB-codes constitute a large group of cyclic codes designed on a combinatorial models with selection of corresponding relationships between the parameters of the code to achieve its specified technical characteristics. Noise protected monolithic and group codes belong to the group of self-correcting codes with a ring structure and probabilistic assessment of the level of noise protection. This property allow so instant lydetect a particular part or all invalid characters in the code word by the majority principle. Mathematical calculations have been performed to calculate the optimized ratios between the parameters of cyclic IRB-codes, under which they reach maximum correction capacity. The algorithm of constructing and increasing the power of coding methods of optimized noise-resistant IRB-codes is examined and analyzed. The concrete examples of increase efficiency of combinatorial optimization cyclic codes methods with appropriate calculations and tables are given. The comparative analysis of the IRB-codes with the Golay codes and Bose – Chaudhuri – Hocquenghe (BCH) codes with respect to correction ability, power encoding method and computational complexity of decoding procedures is carried out. The advantages and disadvantages of cyclic, and ringmonolithic and group IRB-codes in comparison with classical analogues are determined. The prospect so fusing the research results in the problems of information and communication technologies are outlined.