# 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’

### 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

Thank you