On the computation of the automorphisms group of low density parity check codes using genetic algorithm

Abstract

The genetic algorithm (GA) is an adaptive metaheuristic search method based on the process of evolution and natural selection theory. It is an efficient algorithm used for solving the combinatorial optimization problems, e.g., travel salesman problem (TSP), linear ordering problem (LOP), and job-shop scheduling problem (JSP). The simple GA applied takes a long time to reach the optimal solution, the configuration of the GA parameters is vital for a successful GA search and convergence to optimal solutions, it includes population size, crossover operator, and mutation operator rates. Also, very recently, many research papers involved the GA in coding theory, In particular, in the decoding linear block codes case, which has heavily contributed to reducing the complexity, and guaranting the convergence of searching in fewer iterations. In this paper, an efficient method based on the genetic algorithm is proposed, and it is used for computing the Automorphisms groups of low density parity check (LDPC) codes, the results of the aforementioned method show a significant efficiency in finding an important set of Automorphisms set of LDPC codes.