Problems of Syndrome Decoding of Block Error Correction Codes
Vladimir Y. Mikhaylov, Roman B. Mazepa, E. V. Vitomsky · 2024
Object of consideration are linear block error correction codes. The subject of the analysis is syndrome decoding procedures of block codes and effectiveness evaluation of options for their implementation. The purpose of the analysis is to increase the temporal effectiveness of codecs by choosing the code components and reducing the cost of the implementation of decoders on the existing element base. It is easier to evaluate the temporary costs of transmission and processing in codecs for classic relatively short block codes than for long ones due to their good knowledge and relatively visible set of known processing methods. On the other hand, classic codes often have a corrective potential exceeding standard average estimates. The implementation of this potential is currently an urgent task for radio control systems. The problem of long codes is the absence of strong tools for a comparative evaluate of temporary and hardware costs for a large number of various codecs. This limits the competitive possibilities. This work analyzes options for using block codes, including cascading codes. Practical interest in syndrome decoding codes is argued due to the greater elaboration of this direction for the intensive optimization of block codes in terms of their length and decoding efficiency. A constructive approach to solving the problem of optimizing syndrome decoders of cyclic codes is shown. The most important advantage of cyclic codes in relation to other codes is not only the simplicity of their technical implementation. The variety of options for the mathematical description of binary cyclic codes, first of all, with the algebraic apparatus of Galois fields, allows you to introduce and apply unambiguous evaluative metrics of the schematic technological implementation of codecs, which contributes to the creation, development and use of flexible iterative decoding procedures. This article is aimed at attracting the attention of specialists to the problem of the usefulness of describing and analyzing a separate class of objects of a general subject area in the language of a strict unified theory, as well as improving the fast transformations.