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. Coding theory deals with the properties of codes and thus with their fitness for a specific application. ... The binary numeral system represents numeric values using two symbols, typically 0 and 1. ... A Communications channel (or channel for short), models the medium through which information is transmitted from a sender (or transmitter) to a receiver. ... This article is about the unit of information. ... The word probability derives from the Latin probare (to prove, or to test). ... In medicine, a persons pulse is the throbbing of their arteries as an effect of the heart beat. ...
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. Without loss of generality or simply WLOG is a frequently used expression in mathematics. ...
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