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Channel Capacity

Shannon's fundamental limit on reliable communication

C = B · log₂(1 + S/N)
Channel Capacity = Bandwidth × log₂(1 + Signal-to-Noise Ratio)

Channel Parameters

20 MHz
10 mW
1 mW
SNR
10 (10 dB)
Maximum Channel Capacity
69.2 Mbps

Capacity vs SNR (Fixed Bandwidth)

Shannon's Channel Capacity Theorem (1948)

The Fundamental Limit: Shannon proved that reliable communication is possible at any rate below C, but impossible above C, regardless of coding scheme.

Bandwidth Tradeoff: You can trade bandwidth for SNR. Double the bandwidth = double the capacity. Double the SNR = much less capacity gain.

Approaching Capacity: Modern codes (Turbo, LDPC) come within 0.1 dB of Shannon limit!

Real Examples:

• Wi-Fi 6: 160 MHz × log₂(1+~30dB) ≈ 1.6 Gbps theoretical

• 5G NR: 100 MHz × log₂(1+~25dB) ≈ 800 Mbps per antenna