What happen if 0 and 1 are transmitted simultaneously with BPSK?
If you were lucky enough that the carriers were coherent (same phase and frequency) then the received complex symbols would cancel and you would get a zero (plus noise).  However, it is far more likely that the carrier waves will have slightly different frequencies as oscillators will drift.  Since the recevier can only lock on to one of the carriers, one symbol will be received in the proper location and the other one will be spinning around the complex plane.  The sum of the two will end up drawing an arc on the complex plane with the length proportional to the symbol period and frequency offset.  Most likely the ultimate result would be one or more bit errors that would either be corrected in FEC or trigger a retransmit when the checksums do not match.