Binary symmetric channel

A binary symmetric channel (or BSC_p) is a common communications channel model used in coding theory and information theory. In this model, a transmitter wishes to send a bit (a zero or a one), and the receiver will receive a bit. The bit will be "flipped" with a "crossover probability" of p, and otherwise is received correctly. This model can be applied to varied communication channels such as telephone lines or disk drive storage.

The noisy-channel coding theorem applies to BSC_p, saying that information can be transmitted at any rate up to the channel capacity with arbitrarily low error. The channel capacity is ${\displaystyle 1-\operatorname {H} _{\text{b}}(p)}$ bits, where ${\displaystyle \operatorname {H} _{\text{b}}}$ is the binary entropy function. Codes including Forney's code have been designed to transmit information efficiently across the channel.