Abstract
In the literature of Error Correcting Codes (ECC) there are many probabilistic characterizations of different events that happen in the decoding process. Historically, the most considered parameters in the performance of a linear code are the Probability of Undetected Error and the probability of incorrect decoding, also known as Probability of Miscorrected Error. While there is agreement about the first, starting from the Seventies, basically four definitions of the Probability of Miscorrected Error are present in literature; aim of this work is to show that they are equivalent and, although different in the mathematical formulation, they yield exactly the same result. The gap of this missing proof is herein fulfilled and two examples with interesting properties are given. © 2017, Springer International Publishing AG.