Binary Symmetric Channel - Definition

Definition

A binary symmetric channel with crossover probability p denoted by, is a channel with binary input and binary output and probability of error p; that is, if X is the transmitted random variable and Y the received variable, then the channel is characterized by the conditional probabilities

Pr( Y = 0 | X = 0 ) = 1 − p
Pr( Y = 0 | X = 1) = p
Pr( Y = 1 | X = 0 ) = p
Pr( Y = 1 | X = 1 ) = 1 − p

It is assumed that 0 ≤ p ≤ 1/2. If p > 1/2, then the receiver can swap the output (interpret 1 when it sees 0, and vice versa) and obtain an equivalent channel with crossover probability 1 − p ≤ 1/2.

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