Channels · Entropy

Binary symmetric channel

A channel that flips each bit with probability p has capacity C = 1 − H(p) bits per use, which falls from 1 at p = 0 to 0 at p = 0.5, where the output is a coin flip independent of the input.

Builds on Biased coin entropy. Taught in Bits & Surprise.

Raise the flip probability and watch bits stream through a noisy zone that flips some of them, the observed flip rate settle toward p, and the capacity readout fall along the curve 1 − H(p).

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