application of probability on optical communication system

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Seminar on “Application of probability theory in an optical communication system” by Tabassum unnisa 1st sem ,Mtech, Digital communication.: 

Seminar on “Application of probability theory in an optical communication system” by Tabassum unnisa 1 st sem ,Mtech, Digital communication .

Block diagram of optical communication system: 

Block diagram of optical communication system Data input{0,1} {0,1} Laser or LED Photo detector (electrons counter) Decision device

PMF of Poisson random variable : 

PMF of Poisson random variable K=1,2,3…. K=1,2,3….

      : 

Posterior probability Using theorem of total probability

The probabilities of ‘0’ and ‘1’ sent are taken to be equal i,e 1/2: 

The probabilities of ‘0’ and ‘1’ sent are taken to be equal i,e 1/2 So that…

Therefore ,applying Baye’s theorem: 

Therefore ,applying Baye’s theorem

And..for ‘1’: 

And..for ‘1’

Since the dinominator of both posterior probabilities are same,so we decide that 1 was sent if..: 

Since the dinominator of both posterior probabilities are same,so we decide that 1 was sent if.. Or

But sometimes receiver can make wrong decision i,e 0 bit was sent taken as 1 or vice versa. Therefore probability of making an error is given by : 

But sometimes receiver can make wrong decision i,e 0 bit was sent taken as 1 or vice versa. Therefore probability of making an error is given by

  Let x0 be the threshold with which we campare X to dicide which data bit was sent.d: 

Let x0 be the threshold with which we campare X to dicide which data bit was sent.d

Likewise, : 

Likewise, Hence probability of erroe of our optical communication system is given by

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