Probability of erroneous decoding for integer codes correcting burst asymmetric/unidirectional/symmetric errors within a byte and up to double asymmetric errors between two bytes

Abstract

In this paper, we determine the probability of erroneous decoding of integer codes capable of correcting asymmetric CT-bursts, unidirectional solid bursts, and symmetric bursts within a b-bit byte. Also, the probability of erroneous decoding is determined for integer codes correcting single and double asymmetric errors occurring within and between any two b-bit bytes. In order to confirm the validity of the obtained results, we compare some of them with experimental results from the works of other authors. In addition, we analyze how the probability of erroneous decoding changes depending on the bit error rate and the code rate. The study ends with a result based on undetected errors for codes correcting asymmetric CT-bursts.