Uma abordagem exploratória de códigos de correção de erros baseados em Hamming matricial

Abstract

In recent years, with the increasing miniaturization process of electronic components, semiconductors with billions of transistors have been developed. Such technological advances have led to the advancement of more and more effective systems, some of which are intended for space applications, in which the environment is totally hostile to electronic components. Evolution has also made memories faster and with nanometric scales operating at high frequencies and low energy consumption, bringing concerns to the designers of these systems, as errors can affect these components. Such errors can be single bit or burst errors, which makes the whole set vulnerable, if no fault tolerance technique is applied. Thus, error correction codes (ECC) prove to be quite efficient for the correction of errors in bits, with a low cost of execution. Hence, the present work proposes the exploration of organization, algorithms and error correction capability through spatially organized codes using the Hamming code. The study aimed to find out how to obtain better error correction rates in bits by varying the organization of code words plus an associated redundancy in organizational matrices. Using Hamming codes (8.4) and (13.8) and different data organizations, coding and different forms of decoding have been developed, using the Java programming language, to improve the error correction rates in bits. The results were better data correction rates with 100% correction for errors of 2 (two) and 3 (three) bits of data in some orderings. In addition, the last data organization corrected almost 100% for errors in 4 (four) bits of data, which shows that we can go even further in order to obtain better error correction rates in data bits. Besides better error correction rates, the exploration brought a lot of knowledge with respect to the spatial organization of the data and also to how we can advance exploratory studies using matrix codes.