Carleton University
SYSC 5504
Department of Systems and Computer Engineering
ELG 6154
Principles of Digital Communications
Fall 2010/11
Assignment #3
Due on Tuesday, November 16, 2010
1. Suppose the following signalling scheme is used for transmission over an AWGN channel with singlesided noise
power spectral density of
N
0
.

±
6
?
φ
0
(
t
)
φ
1
(
t
)
−
3
A
−
AA
3
A
−
3
A
−
A
A
3
A
s
000
s
001
s
111
s
110
s
100
s
101
s
011
s
010
(a) Carefully draw the boundaries of the optimal decision regions in the signal space diagram. Be precise.
(b) Use the union bound to Fnd a tight upper bound the probability of a symbol error. Express your answer in
terms of
N
0
and the average transmitted energy per symbol (
E
s
).
2. ±ind the capacity of the following binary channel, expressing your answer in terms of a rational number.
0
1
0
1
XY
1/2
1/2
1/4
3/4
3. Suppose the linear (
n, k
) block code deFned by the generator matrix
G
=
⎡
⎣
100101
010110
001011
⎤
⎦
is used for error detection. Transmission is carried out over an AWGN channel with BPSK with
E
b
/
N
0
equal to 7
dB.
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 Spring '10
 HUANG
 Coding theory, Hamming Code, Error detection and correction, error detection, AWGN Channel

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