Binary symmetric channel
- A binary symmetric channel (or BSC) 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 receives a bit.
- It is assumed that the bit is usually transmitted correctly, but that it will be "flipped" with a small probability (the "crossover probability").
- This channel is used frequently in information theory because it is one of the simplest channels to analyze.
- 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 = 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.
- This channel is often used by theorists because it is one of the simplest noisy channels to analyze. Many problems in communication theory can be reduced to a BSC.
- Conversely, being able to transmit effectively over the BSC can give rise to solutions for more complicated channels.