Shannon Capacity (for noisy channels)

• Definition: Shannon’s theorem calculates the maximum bit rate of a channel with noise, factoring in the Signal-to-Noise Ratio (SNR).

• Formula: Shannon Capacity = Bandwidth×log2(1+S/N), where S/N is the signal-to-noise ratio.

  Bandwidth×log⁡2(1+S/N) ext{Bandwidth} imes \log_2(1 + ext{S/N})

  S/NS/N

• Interpretation: Higher signal-to-noise ratios or bandwidths increase the data rate. However, the presence of noise limits this capacity.

• Example: With a 3000 Hz bandwidth and an S/N ratio of 30, the Shannon Capacity is 3000×log2(1+30)≈14,907 bps.

  3000×log⁡2(1+30)≈14,907 bps3000 imes \log_2(1 + 30) pprox 14,907 ext{ bps}

Notes

References