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# Z-channel (information theory)

In information theory, a Z-channel with crossover probability p is a binary-input-binary-output channel that flips the input bit 0 with probability p, but maps input bit 1 to 1 with probability 1. The Z-channel has a capacity of

$log_2left\left(1+\left(1-p\right) p^\left\{p/\left(1-p\right)\right\}right\right) ,$

bits per channel use. For small p, the capacity is approximated by

$1- 0.5 H\left(p\right) ,$

where H(p) is the binary entropy function.

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