Fig. S2.

Method used for BER calculation. The two curves are Gaussian with average ${\mu }_1$ and ${\mu }_0$ and SD ${\sigma }_1$ and ${\sigma }_0$ for on- (blue) and off- (red) channels, respectively. C is the crossing of the two curves and is set as the criterion to judge if the signal is on or off. The error bits are on-channels below C and off-channels above C. The BER is given by the ratio of the green area and the area below the two curves.