Boston University
Department of Electrical and Computer Engineering
ENG EC515 Digital Communication (
Fall 2009
)
Problem set 3
Assigned:
Mon 5 Oct
Due:
Mon 12 Oct
Suggested reading:
Classnotes, handouts, and Ch. 4 textbook
O
ffi
ce hours:
M, W 4:00–5:30pm PHO438
Problem 3.1
(Optimum receiver)
A communication system is used to transmit one of two equally likely messages,
M
∈ M
=
{
1
,
2
}
. The
channel output is a voltage (a continuous random variable),
Y
∈
R
, whose conditional density function is
given by:
p
Y

M
(
y

1)
=
y
0
≤
y
≤
1
2

y
1
≤
y
≤
2
0
otherwise
p
Y

M
(
y

2)
=
(
0
.
25

1
≤
y
≤
3
0
otherwise
(a)
Determine
b
m
opt
(
y
) the optimum (minimum probability of error) receiver decision rule.
(b)
Compute
P
e
the resulting probability of error.
Problem 3.2
(
Value of noisy look at noise)
A communication system is used to transmit one of two equally likely messages,
M
∈ M
=
{
1
,
2
}
. The
channel inputs are voltage levels (real numbers). The channel encoder uses a real channel codebook con
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '09
 VenkateshSaligrama
 Normal Distribution, Probability theory, Boston University Department of Electrical and Computer Engineering, equally likely messages

Click to edit the document details