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TELCOM 2120: Network Performance
Fall 200
9
Homework 1 Solution
Problem 1 (5 points)
Consider a binary digital communication channel. To transmit a digital 0 the sender
places a voltage of 1 volt on the channel for the symbol duration time. To transmit a
digital 1 the sender places a voltage of +1 volt on the channel for the symbol duration
time. The receiver detects the symbol on the communication channel as signal Y = v +
N where v is 1 or 1 volt depending on the symbol transmitted and N is Gaussian white
noise which is modeled as a Normally distributed random variable with mean 0 and
variance 4. The receiver decides a 0 was sent if the voltage Y is negative and a 1
otherwise.
(a) Find the probability of the receiver making an error if a digital 0 is sent.
v is 1 when a digital 0 is transmitted. The receiver would make an error when Y > 0.
That happens when N > 1. Since N is normally distributed with zero mean and
variance 4,
Pr[N > 1] = 1  Pr[N
≤ 1]
= 1  Pr[Z
≤ (1

μ
) /
σ
]
= 1  Pr[Z
≤ (1
 0) /
√
4]
= 1 – (0.5+0.1915)
= 0.3085
(b) What is the probability of making the correct decision if a digital 1 is transmitted?
v is +1 when a digital 1 is transmitted. The receiver would make a correct decision when
Y > 0. That happens when N > 1. Using the similar approach,
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 Spring '09

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