Evaluation of permutation decoding tools according to the criterion of the code energy gain

The article presents the result of a numerical experiment held in order to evaluate the asymptotic parameters of the energy gain of a redundant code under conditions of a change in the signal-tonoise ratio for various methods of processing the received code vector by the receiver. The theorem of equivalence of the energy gain of the code is formulated and proved in the conditions of a virtual request for repetition of combinations of redundant code, for which a single permutation of the columns of the information part of the equivalent code generating matrix proved unacceptable. Comparative estimates of the results of decoding code vectors in a permutation decoding system with a system for which traditional algebraic decoding is used are provided. New data on the structure of substitutions for a number of block systematic codes are presented for the revealed features of the organization of the procedure for correcting the rearranged matrix of the equivalent code. Based on a direct enumeration of possible permutations and an assessment of the non-degeneracy property of rearranged matrices, recommendations on the organization of a permutation decoding algorithm for the analyzed code structures are given.