ФРАКТАЛЬНАЯ КЛАСТЕРИЗАЦИЯ ГРУППОВЫХ КОДОВ В СИСТЕМЕ ВЛОЖЕННЫХ ПОЛЕЙ ГАЛУА

Abstract

The permutation decoding (PD) of group systematic noise-immune codes is proved to be the most efficient method in using the redundant data entered to the code as against other methods of decoding digital data [1-5]. This opens up the opportunity of solving a complex computational problem of finding an equivalent code (EC), which is used to search for the error vector. The essence of this solution is that the computational procedure of real-time search for EC for each new combination of redundant code is replaced by a preliminary process of training the decoder to put in accordance with each new permutation of characters the generating matrix of EC parameters, which are recorded in the decoder’s memory card during training. Thus, such a memory card is called a cognitive card (CC). The article estimates the memory size of the CC, when using the block code (15,7,5), and shows the possibility of implementing a permutation decoder on basis of existing integrated circuits based on proven statements. For the first time, the apparatus of fractal partitioning of augmented binary Galois fields using the clustering of the common space of code vectors of a given code is used to prove the main statements. An efficient algorithm is presented to search for a set of invertible matrices of rearranged codes that do not provide an EC and for this reason should be primarily detected in the decoding procedure of the received code vectors.