Channel capacity

Information theory · Formula · Not yet linked from a lesson

C=max⁡p(x)I(X;Y)C = \max_{p(x)} I(X; Y)

The highest rate at which information can cross a noisy channel with errors driven arbitrarily low. Shannon's result is that below this rate reliable communication is possible and above it is not — with no gentle slope in between.

Symbols

CC
The capacity, in bits per channel use.
I(X;Y)I(X; Y)
The mutual information between input and output.
max⁡p(x)\max_{p(x)}
Maximised over every way of choosing inputs.
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