Z-channel (information Theory) - Definition

Definition

A Z-channel (or a binary asymmetric channel) is a channel with binary input and binary output where the crossover 1 → 0 occurs with nonnegative probability p whereas the crossover 0 ← 1 never occurs. In other words, if X and Y are the random variables describing the probability distributions of the input and the output of the channel, respectively, then the crossovers of the channel are characterized by the conditional probabilities

Prob{Y = 0 | X = 0} = 1
Prob{Y = 0 | X = 1} = p
Prob{Y = 1 | X = 0} = 0
Prob{Y = 1 | X = 1} = 1−p

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