Binary Erasure Channel

In information theory and telecommunications, an erasure channel is a communication channel model wherein errors are described as erasures.

Binary Erasure Channel Model.

Binary Erasure Channel Model

The BEC is a binary channel; that is, it can transmit only one of two symbols (usually called 0 and 1).
(A non-binary channel would be capable of transmitting more than two symbols, possibly even an infinite number of choices.)
The channel is not perfect and sometimes the bit gets "erased"; that is, the bit gets scrambled so the receiver has no idea what the bit was.

A binary erasure channel with erasure probability Pe is a channel with binary input, ternary output, and probability of erasure Pe.
That is, let X be the transmitted random variable with alphabet {0, 1}.
Let Y be the received variable with alphabet {0, 1, e}, where e is the erasure symbol.
Then, the channel is characterized by the conditional probabilities

The channel model for the binary erasure channel showing a mapping from channel input X to channel output Y (with known erasure symbol ?). The probability of erasure is Pe

从概率的角度理解

References:

Suayb S. Arslan,. Incremental Redundancy, Fountain Codes and Advanced Topics (PDF). 2014.
https://en.wikipedia.org/wiki/Binary_erasure_channel