Open AccessNOISE IMMUNITY OF THE ALGEBRAIC GEOMETRIC CODES
Author(s) -
Alexandr Кuznetsov,
Євгенія Колованова,
Олексій Смірнов,
Тетяна Кузнецова
Publication year - 2019
Publication title -
computing
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.184
H-Index - 11
eISSN - 2312-5381
pISSN - 1727-6209
DOI - 10.47839/ijc.18.4.1610
Subject(s) - block code , noise immunity , algebraic number , decoding methods , coding (social sciences) , algebraic curve , noise (video) , computer science , transmission (telecommunications) , mathematics , geometric networks , discrete mathematics , linear code , algorithm , theoretical computer science , telecommunications , combinatorics , mathematical analysis , graph theory , statistics , artificial intelligence , image (mathematics)
Linear block noise-immune codes constructed according to algebraic curves (algebraic geometric codes) are considered, their design properties are evaluated, algorithms of construction and decoding are studied. The energy efficiency of the transmission of discrete messages by M-ary orthogonal signals in the application of algebraic geometric codes is studied; the achievable energy gain from the use of noise-immune coding is estimated. The article shows that in discrete channels without memory it is possible to obtain a significant energy gain, which increases with the transition to long algebraic geometric codes constructed from curves with a large number of points relative to the genus of the curve. It is found that the computational complexity of implementing algebraic geometric codes is comparable to other known noise-immune codes, for example, Reed-Solomon codes and others. Thus, high energy efficiency in combination with the acceptable computational complexity of implementation confirms the prospects of algebraic geometric codes use in modern telecommunication systems and networks to improve the noise immunity of data transmission channels.