Probability of Undetected Error on a Binary Symmetric Channel without Memory via Bayesian Inference

One of the main problems in calculating the probability of undetected error of a linear code on a binary symmetric channel (BSC) is the lack of information about the bit error probability of the channel. To avoid such problems, a new definition of the probability of undetected error is given making use of Bayesian inference, provided the value of the bit error probability can be estimated by means of a sample. The length of the samples tending to infinity, the sequence of the respective undetected error probabilities turns out to be convergent. The results then are related to the problem of meeting a specific safety integrity level (SIL).