The BEC is characterized by the probability of erasure $\epsilon$.

There are two input possibilities {0,1}.

There are three output possibilities {0,1,?}. The “?” sign means that this bit is erased due to the BEC.

The channel transition matrix of a binary erasure channel is as follows:

$$P=\begin{pmatrix} 1-\epsilon& 0\\ \epsilon& \epsilon\\ 0& 1-\epsilon \end{pmatrix}$$

The BEC is very useful in modeling channels with erasures, channels with high Signal to Noise ratio (SNR) and three-level quantization.