Shannon Channel Capacity — BSC & BEC

Every noisy channel has a maximum information rate — the channel capacity C. Below C, arbitrarily reliable communication is possible (Shannon 1948). Above C, errors are unavoidable.

Channel Type

Press "Transmit Bits"

Formulas

BSC: C = 1 − H_b(p)
H_b(p) = −p·log₂p − (1−p)·log₂(1−p)

BEC: C = 1 − ε
(fraction 1−ε arrives; ε erased)

AWGN: C = ½·log₂(1 + SNR)

Shannon: R < C → ∃ code
with P_e → 0 as n → ∞

Current Channel

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