hippke/communication

Interstellar communication

communication's Issues

Issue with the return values of the holevo_perfect and holevo_thermal functions

I believe there is an error in the holevo_perfect and holevo_thermal functions in PyCom.py. In the latter there is the function

def gx(x, eta, M):
return (((1 + x)) * log2(1 + x) - x * log2(x)) / M * eta

whereas I believe it should be

def gx(x, eta, M):
return (((1 + x)) * log2(1 + x) - x * log2(x)) / (M * eta)

That is, the current function is multiplying by eta, not dividing by eta. I believe the division by (M*eta) is correct, as it would ensure that holevo_thermal returns the bits per detected photon. I think this effects some results in the paper https://doi.org/10.1017/S1473550417000507
For example, the value for C_th quoted in Figure 9 would then become 4 bits per (detected) photon (instead of 1) at N_M=0.13, M=1e-5, eta=0.5 (and the plotted curve is then also offset). With eta=0.5, some other results for the capacity (bits per detected photon) may be too low by a factor of 4 (and bits per incident photon by a factor of 2).