Decoding of systematic group codes based on fractal clustering of Galois fields

• Published in: AIP conference proceedings Vol. 2787; no. 1
• Main Authors: Gladkh, Anatoliy A., Attaby, Aqeel L., Al-Mesri, Ali S.
• Format: Journal Article Conference Proceeding
• Language: English
• Published: Melville American Institute of Physics 14.07.2023
• Subjects: Algorithms; Clustering; Codes; Decoding; Digital data; Fractals; Integrated circuits; Matrices (mathematics); Memory; Permutations; Redundancy; Searching; Symbols
• ISSN: 0094-243X; 1551-7616
• DOI: 10.1063/5.0148054

It is proved that permutation decoding (PD) of group systematic noise-resistant codes are able to ensure the use of redundancy introduced into the code to the greatest extent in comparison with other methods of decoding digital data. The peculiarity of such a solution is that the computational procedure of real-time search for an equivalent code (EC) for each new combination of the used code. Therefore, for each permutation of symbols, it is advisable to have pre-calculated generating matrices of the EC recorded in a special memory card of the decoder. Therefore, such a memory card was called a cognitive card (CC). The article estimates the amount of CC memory when using the Bose-Chowdhury-Hockingham block code (BCH) (15, 7, 5). An algorithm is proposed for searching for a complete set of unproductive permutations (NP) of code vector symbols to obtain a complete cognitive decoder map (CCDM) using a PYTHON software product. Based on the proven statements, the possibility of implementing a permutation decoder based on existing integrated circuits is shown. For the first time, the apparatus of fractal partitioning of extended binary Galois fields using the clustering method of the common space of code vectors of a given code is used to prove the main statements. On this theoretical basis, an effective algorithm is presented for searching for a set of degenerate matrices of rearranged codes that do not provide EC and for this reason should be detected in the decoding procedure of the received code vectors out of any queue.