The performance of digital receiver is measured by a parameter called the Bit-Error Ratio (BER). The BER tells the fraction of the bits which are wrongly detected,i.e.
For a satisfactory performance the BER has to be less than .
The Figure shows the signal current when bit-0 is transmitted and when bit-1 is transmitted. The figure also shows the probability density function of the current in the two binary states.
For BER calculation it is assumed that the noise is almost Gaussian with standard deviations and , and means respectively for the 0 and 1 binary levels. For an optical receiver, in general the two standard deviations are different. For thermal noise dominated regime the two become same.
The decision threshold is . That is
So a bit error occurs
when bit-0 is transmitted and.
When bit-1 is transmitted and .
The BER for an unbiased data ( a data which has statistically equal number of 0 and 1 bits), the BER is given as
where is the probability of error in bit-1, i.e. probability of current remaining below the threshold when actually bit-1 has been received.
is the probability of error in bit-0, i.e. probability of current becoming greater than or equal to the threshold when actually bit-0 has been received.
. 
and 
, and means 
respectively for the 0 and 1 binary levels. For an optical receiver, in general the two standard deviations are different. For thermal noise dominated regime the two become same. 
. That is 
. 
. 
is the probability of error in bit-1, i.e. probability of current remaining below the threshold when actually bit-1 has been received. 
is the probability of error in bit-0, i.e. probability of current becoming greater than or equal to the threshold when actually bit-0 has been received. 
