Shannon Capacity, Eb/N0 & BER
Ties together the fundamentals of a digital link. From the bandwidth and SNR it gives the Shannon capacity — the theoretical maximum error-free bit rate — and the spectral efficiency. It converts between SNR and the per-bit energy ratio Eb/N0 using your bit rate, and computes the bit error rate for coherent BPSK/QPSK. Enter either SNR or Eb/N0.
Equations & Parameters ▸
\(C = B\log_2(1+\text{SNR}) \qquad \dfrac{E_b}{N_0} = \text{SNR}\cdot\dfrac{B}{R_b}\)
\(\text{BER}_{\text{BPSK/QPSK}} = Q\!\left(\sqrt{2E_b/N_0}\right),\quad Q(x)=\tfrac{1}{2}\operatorname{erfc}\!\left(\tfrac{x}{\sqrt2}\right)\)
\(\text{BER}_{\text{BPSK/QPSK}} = Q\!\left(\sqrt{2E_b/N_0}\right),\quad Q(x)=\tfrac{1}{2}\operatorname{erfc}\!\left(\tfrac{x}{\sqrt2}\right)\)
| B | Channel bandwidth (Hz). |
| Rb | Information bit rate (bit/s). |
| SNR | Signal-to-noise ratio in the bandwidth B (dB). Enter this or Eb/N0. |
| Eb/N0 | Energy per bit to noise power spectral density (dB). Enter this or SNR. |
| C | Shannon capacity — the maximum error-free rate. A link is feasible only if Rb < C. |
References: C. E. Shannon, "A mathematical theory of communication," Bell Syst. Tech. J., 1948. · J. G. Proakis & M. Salehi, Digital Communications, 5th ed., McGraw-Hill, 2008.
Inputs
Hz
Channel BWbit/s
Data ratedB
In bandwidth BdB
Per-bit ratioFor BER
Results
Capacity
Shannon capacity—
Spectral eff. (C/B)—
Link eff. (Rb/B)—
Link quality
SNR—
Eb/N0—
BER—
Diagram