Hi urwelcome, To be honest I dont know the exact answer for your question but to me the formula C=B*log(1+SNR) gives only an upper limit. It is not directly related with Gaussian. Yes it is calculated by assuming a gaussian distribution and I hope you somehow can calculate it for other distributions but in fact it says: the highest Rate that you can achieve using a communication system is C=B*log(1+SNR) whether it is gaussian distributed or not.
Like you have said, capacity is achieved when input to the AWGN channel is gaussian distributed. Thus, when input in not gaussian, capacity is NOT achieved. So the question on what is the capacity when input is equi-probable binary is incorrect, AFAIK.
You can only say that with this binary signalling scheme, you chose to operate the channel with a rate lower than capacity.
-b