From literature, some results are well known. For example:

• Bipolar channel, average power constraint:
  $$C_{bip} = \frac{1}{2} \log_2\left(1 + \frac{1}{\sigma_n^2} \right)$$ obtained with input distribution $$p_X(x) = \frac{1}{\sqrt{2\pi}\sigma_n}\exp\left(-\frac{1}{2}\frac{x^2}{\sigma_n^2}\right)$$
• Unipolar channel, average amplitude constraint:
  approximation for $\sigma_n^2\ll 1$ is $$C_{unip} = \frac{1}{2}\log_2\left(1+\frac{e}{2\pi\sigma_n^2} \right)$$ obtained with input distribution $$p_X(x) = \begin{cases} \exp\left(-x\right) & x\geq0 \\ 0 & x<0 \end{cases}$$

Both characteristics are used as a reference in the following.