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INTRODUCTION Optical communication also known as optical telecommunication, is communication at a distance using light to carry information. It can be performed visually or by using electronic devices. Photophone is one of the example of electronic devices use for optical communication. An optical communication system uses a transmitter, which encodes a message into an optical signal, a channel, which carries the signal to its destination, and a receiver, which reproduces the message from the received optical signal.
BLOCK DIAGRAM
Laser or Led
Photo detector
Decision
Data Input {0,1} {0,1}
Channel
APPLICATION OF PROBABILITY • In optical communication, the receiver must convert the
optical signal back into a string of binary numbers using photo detector. The received light wave strikes photo massive surface, which emits electrons in a random manner. While the number of electrons emitted during a T second interval is random and thus needs to be described by a random variable, the probability mass function of that random variable changes according to intensity of light on photo missive surface during the T second interval. We will use conditional probability and poisson random variables, Total probability and Bayes’s theorem.
We define random variable X to be the number of electrons counted during time interval T. Now here we describe random variable in terms of two conditional probability mass function,
,.......,2,1,0,!
)(
,.......,2,1,0,!
)(
1
0
1
1|
0
0|
kk
eRkP
kk
eRkP
Rk
X
Rk
X
• Now using Total Probability Theorem
)1Pr()()0Pr()()Pr()( 1|0| sentkPsentkPkXkP XXX
• The a priori probabilities Pr (0 sent) and Pr (1 sent) are to be taken equal to (1/2)
• Therefore, applying Baye’s theorem,
1010 2
1
2
1)( RkRk
X eReRkP
10
0
!21
!21
21
)(
)0Pr()(k)X|sent0Pr(
10
00|
RR
R
ekR
ekR
eR
kP
sentkPkk
k
X
X
CONTD..
10
1
!21
!21
21
)(
)1Pr()(k)X|sent1Pr(
10
11|
RR
R
ekR
ekR
eR
kP
sentkPkk
k
X
X
CONTD..
• Since the denominators of both a posteriori probabilities, are same, we decide if sent if,
• After, a little algebraic manipulation this reduces down to choosing in a favor of a 1 if,
01
!2
1
!2
1 01 Rk
Rk
ek
Re
k
R
)/ln( 21
01
RR
RRk
• The receiver for our optical communication system counts the number of electron emitted and compares that number with threshold.
• If the number of electrons emitted is above the threshold, we decide that a 1 was sent; otherwise, we decide a 0 was sent.
ERROR ANALYSIS
• Errors can occurs in two manners.• A 0 could be sent initially. However, if the number of
electrons exceeds the threshold value, it may be counted as 1.
• Similarly, 1 could be sent initially. However, if the number of electrons does not reach the threshold value, it may be considered as 0.
• Now, applying the concept of conditional probability.
• Let x0 be the threshold with which we compare X to decide which data bit was sent.
• 1 was sent if X>x0 and a 0 was sent if X<x0.
)1Pr()1|Pr()0Pr()0|Pr()Pr( sentsenterrorsentsenterrorerror
IF 0 WAS SENT
1
0|0
0
)( sent) 0|Pr( sent) 0 |(errorPrxk
X kPxX
0
00
0 0
0
1
0
!1
!
x
k
Rk
R
xk
k
ek
Re
k
R
IF 1 WAS SENT
0
1
0
0
1
00| !
)( sent) 1|Pr(errorx
k
Rkx
kX e
k
RkP
• Hence probability error of our optical communication system is
0 10
0
10
!2
1
2
1 Pr(error)
x
k
RkRk
k
eReR
GRAPHICAL ANALYSIS AND REPRESENTATION• We can plot probability of error as a function or R0 and R1.
• Where R0 is a characteristic of photo diode used and can be interpreted as the average number of electron emitted during a bit interval when there is no signal incident on the photodetector.
• And, R1 controlled by intensity of incident light.
• The intensity of Laser or the LED can be adjusted to produce the required value for the parameter R1.
Probability of error curves for an optical communication system
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