Binary erasure channel

The binary erasure channel (BEC) with parameter $\epsilon$ is the channel with input $X \in \{0, 1\}$, output $Y = \{0, 1, ?\}$, and transition probabilities \begin{align*} p_{Y \mid X}(y \mid x) = \begin{cases} 1-\epsilon, & x=y, \\ \epsilon, & y=?, \\ 0, & \text{else}. \end{cases} \end{align*} In 1954, Elias introduced the erasure channel as a toy example. It is now a useful model for many information theory problems including packet loss in the internet.