Binary symmetric channel

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In coding theory, a binary symmetric channel (or BSC) is an idealized model of a communications channel that sends bits. In a BSC, the probability of a 1 becoming a 0 and of a 0 becoming a 1 are assumed to be the same (hence the term symmetric). Since 1s and 0s may be represented very differently (as a pulse and absence of a pulse, for instance), this assumption is often not valid in practical situations. However, this assumption makes analysis much easier.

Formally, let p < ½ be the probability of an error occurring. Then the probability of a bit sent over a BSC being correctly received is (1−p), and this probability is independent of what bit is sent. Assuming that p is known to the receiver, we may without loss of generality assume that since otherwise we may simply invert (swap over) the received symbols giving an error probability of 1 − p < 1 / 2. The story is more subtle if p is entirely unknown to the receiver.