COSC 4214: Digital Communications
Assignment # 4: Channel Coding
Coverage: Section 6.1 – 6.7, Sections 7.1 – 7.3
Due Date: November 29, 2006
Problem 1 (Probability of Symbol Error):
Calculate the probability of message error for a 12bit data
sequence encoded with a (24, 12) linear block code. Assume that the code corrects all 1bit and 2bit error
patterns and assume that it corrects no error patterns with no more than two errors. Also, assume that the
probability of a channel symbol error is 10

3
.
Problem 2 (BPSK with linear block code):
Calculate the improvement in probability of message error relative
to an uncoded transmission for a (24, 12) doubleerrorcorrecting linear block code. Assume that coherent BPSK
modulation is used and that the received
E
b
/
N
0
= 10 dB.
Problem 3 (Linear Block Code):
Design an (7, 4) linear block code whose generator matrix is given by
=
1
0
0
0
0
1
1
0
1
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
1
1
1
1
G
by solving the following questions.
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 Spring '08
 Staff
 Coding theory, Hamming Code, Error detection and correction, linear block code

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