Using a genetic algorithm to find good linear error-correcting codes

Abstract

A genetic algorithm is used to search for linear binary codes with optimal minimum distance for a fixed length n and dimension k. Several modifications to the algorithm are compared to find an algorithm best suited to this application. The code is parallelized and mn on a multi-processor and speedup determined.

Evolutionary Strategies for the Design of Binary Linear Codes

“…McGuire and Sabin [4] employed a GA to search for linear codes. To enforce the linearity of the evolved codes, the genotype of the candidate solutions were k•n bitstrings, which represented the concatenation of the rows of k×n generator matrices.…”

“…3, most of the works addressing the design of errorcorrecting codes via metaheuristic algorithms usually target generic codes without any constraint on their linearity. The only exception seems to be the paper by McGuire and Sabin [4] where a GA evolves a generator matrix, but there is no control on the dimension k of the corresponding code. As a matter of fact, if one applies unrestricted variation operators on a matrix of rank k (such as one-point crossover or bit-flip mutation), then the vectors in the resulting matrix might not be linearly independent, and thus the associated code could have a lower dimension.…”

“…Concerning the combinations of length n, dimension k, and minimum distance d of the codes, we experimented over five problem instances: (12,6,4), (13,6,4), (14,7,4), (15,7,5), and (16,8,5). In particular, we always set k = n/2 since this gives the largest search space possible for a given n. Starting from n = 12 yields the smallest instance that is not amenable to exhaustive search.…”

“…The design of a good binary code is a combinatorial optimization problem where the objective is to maximize the minimum distance of a set of codewords, and it is equivalent to finding a maximum clique in a graph [2]. Several optimization algorithms have been applied to solve this problem, including evolutionary algorithms [3][4][5][6] and other metaheuristics [5,[7][8][9][10]. Most of these works target the construction of unrestricted binary codes, without any linearity requirement.…”

“…Most of these works target the construction of unrestricted binary codes, without any linearity requirement. The only exception is [4], where genetic algorithms are used to evolve the generator matrices of linear codes, but without preserving their ranks; thus, the dimension of the evolved codes can vary.…”