Can I make photodiode's voltage output bipolar?
You can do this trivially by replacing the 0v rail with your negative rail; the output will thus swing between the negative and positive rails. How close it gets to those rails depends on the light input, your photodiode's characteristics, and the resistor; it will not be a neat square wave, but will require squaring up with a comparator.

Since your data is using NRZ coding, which guarantees you'll see a certain minimum rate of edges, you could also use AC coupling to achieve this without a negative rail:







simulate this circuit &ndash; Schematic created using CircuitLab