Shannon Channel Capacity

Formula

Description

The Shannon-Hartley theorem establishes the theoretical maximum rate at which information can be reliably transmitted over a communication channel with a given bandwidth and signal-to-noise ratio. Published by Claude Shannon in 1948, it is the foundation of information theory and sets an absolute upper bound that no practical modulation or coding scheme can exceed. Real-world systems like Wi-Fi, LTE, and cable modems approach this limit using advanced techniques like OFDM, turbo codes, and LDPC codes.

Variables

• C — Channel capacity in bits per second (bps)
• B — Channel bandwidth in hertz (Hz)
• SNR — Signal-to-noise ratio (linear, not dB)

Practical Notes

To convert SNR from dB to linear: SNR_linear = 10^(SNR_dB/10). Doubling the bandwidth doubles the capacity, but doubling the SNR gives diminishing returns due to the logarithmic relationship. Modern 5G systems achieve near-Shannon capacity through massive MIMO and advanced coding.