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ECEN 455: Assignment 5
Due Monday 11/14/11
Reading:
•
Required: First Course in Digital Communications Chapter 6
Problems:
1. Calculate the probability of message error
P
B
for a 12bit data sequence encoded with a
(24
,
12) linear block code when the probability of a channel symbol error is 10

3
. Assume
that the code corrects all 0bit, 1bit, and 2bit error patterns and that it corrects no other
error patterns.
2. Calculate the improvement in the message error probability
P
B
relative to uncoded trans
mission for a (24
,
12) doubleerror correcting linear block code. Assume coherent BPSK
modulation is used and that
E
b
/N
0
= 10 dB.
3. Consider a (7
,
4) binary code whose generator matrix is
G
=
1 1 1 1 0 0 0
1 0 1 0 1 0 0
0 1 1 0 0 1 0
1 1 0 0 0 0 1
.
(a) Find all codewords in the code.
(b) What is the errorcorrecting capability of the code? What is the errordetecting capa
bility the code?
(c) Find the paritycheck matrix
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