Channel Capacity

Shannon-Hartley Theorem

Maximum rate of reliable communication over a noisy channel:

$$ C = B \log_2\left(1 + \frac{S}{N}\right) $$

Where:

• $C$ = channel capacity (bits/second)
• $B$ = bandwidth (Hz)
• $S/N$ = signal-to-noise ratio

Example

 1import numpy as np
 2
 3def channel_capacity(bandwidth, snr_db):
 4    """Calculate channel capacity"""
 5    snr_linear = 10**(snr_db/10)
 6    return bandwidth * np.log2(1 + snr_linear)
 7
 8# 1 MHz bandwidth, 20 dB SNR
 9C = channel_capacity(1e6, 20)
10print(f"Capacity: {C/1e6:.2f} Mbps")

Further Reading

• Channel Capacity - Wikipedia

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