The relationship between the bit error rate and E<sub>b</sub>/N<sub>0</sub> depends on the modulation scheme and detection type (coherent vs. non-coherent). For example, for coherent QPSK modulation, one can write:
<math> P_b = 0.5 \! ; \text{erfc} \left( \sqrt{ \frac{E_b}{N_0} } \right) </math>
where P<sub>b</sub> is the bit error rate and erfc(x) is the complementary error function.