ECE 5670 : Digital Communications (Spring 2011)
Homework 2
Due February 10 in class
Instructor: Salman Avestimehr
Oﬃce 325 Rhodes Hall
1. Suppose we are employing sequential communication to work at data rate
R
bits per
unit time and error probability
p
e
. In Lecture 2, we saw that doubling the transmit
energy allowed us to either approximately:
•
increase the data rate by 0.5 bits per unit time or
•
improve the reliability by making the error probability equal to
p
2
e
.
Suppose than an engineer wants to increase the data rate
and
increase reliability at
the same time, while still only doubling the transmit energy. The improvements are
as follows:
•
data rate is now
R
+
r
bits per unit time and
•
error probability is now
p
d
e
.
Calculate the entire set of values (
r, d
) can take.
Based on our earlier observation,
this set should include the points (0.5,1) and (0,2).
2. In this exercise we see the tradeoff between data rate and
SNR
while communicating
reliably at certain desired level using the sequential communication scheme.
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 Spring '11
 SCAGLIONE
 Statistics, Normal Distribution, Probability theory, data rate

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