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A binary symmetric channel is a common communications channel model used in coding theory and information theory. In this model, a transmitter wishes to send a bit , 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 BSCp, saying that information can be transmitted at any rate up to the channel capacity with arbitrarily low error. The channel capacity is 1 − H b {\displaystyle 1-\operatorname {H} _{\text{b}}} bits, where H b {\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.