Shannon Channel Capacity
C = B log₂(1 + S/N) bits/s · Channel coding theorem · BSC · BEC
Bandwidth B (kHz):
10
SNR (dB):
20
dB
Channel:
AWGN
BSC
BEC
Error prob p:
0.1
Shannon-Hartley theorem (AWGN):
C = B·log₂(1+S/N) bits/s. Maximum rate for error-free communication.
BSC
(Binary Symmetric Channel): C = 1 − H_b(p) = 1 − (−p·log₂p − (1−p)·log₂(1−p)).
BEC
(Binary Erasure Channel): C = 1 − ε (fraction not erased).
Channel coding theorem:
For R < C, there exist codes with P_error → 0 as block length → ∞. For R > C, P_error → 1 inevitably.