Abstract
Error correcting codes, also known as error controlling codes, are set of codes with redundancy that allows detecting errors. This is quite useful in transmitting data over a noisy channel or when retrieving data from a storage with possible physical defects. The idea is to use a set of code words that are maximally distant from each other, hence reducing the chance of changing a valid codeword to another valid codeword by flipping bits. The problem can be viewed as picking m codes out of 2 n available n- bit combinations, such that the aggregate hamming distance among those codewords is maximized. Due to the large solution spaces of such problems, greedy algorithms are sometimes used to generate quick and dirty solutions. However, modern evolutionary search algorithms like genetic algorithms, swarm particles, gravitational search and others, offer good alternatives, yielding near optimal solutions in exchange for some time. Chemical Reaction Optimization (CRO) has emerged as a new evolutionary algorithm to solve complex optimization problems. This algorithm mimics the molecular interactions towards finding a minimal energy state, which corresponds to an optimal solution for the problem in hand. In this research, we proposed a solution for the maximally distant codes allocation problem, through a binary knapsack mapping and compared the performance with the well established Ant Colony Optimization (ACO) algorithm, which is inspired by the ant's capability to find the shortest path between the nest and source of food. The binary knapsack mapping was used in the two algorithms. Test results showed that the CRO outperformed the ACO in every metric given any time budget.
Highlights
Allocating sets of codes with maximum aggregate mutual distances for use as error control codes is of great significance and finding optimal solutions for practically sized problems using full search is a challenge due to the prohibitively large solution spaces
The solution space of the small instance (7, 16, 3), which requires finding a set of 16 codewords of 7 bits with minimal mutual Hamming distance of 3, is at least 1020, ruling out any exact search methodology
The results showed that an important improvement was achieved with the inclusion of the Repulsion
Summary
Allocating sets of codes with maximum aggregate mutual distances for use as error control codes is of great significance and finding optimal solutions for practically sized problems using full search is a challenge due to the prohibitively large solution spaces. The solution space of the small instance (7, 16, 3), which requires finding a set of 16 codewords of 7 bits with minimal mutual Hamming distance of 3, is at least 1020, ruling out any exact search methodology. We mapped the maximally distant code allocation problem to the well known binary knapsack problem and compared the performance of those two algorithms in finding sets of codewords of various length and cardinality, using a weighted fitness (or cost) function to provide balance between two objectives; mean and minimum distance
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