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1
Error Control Coding Asssignment 1
Due 11:00 am Friday 1 April 2011
Value in brackets indicates marks for each question. Total value of marks is 20. This assign
ment counts towards 12.5% of the total assessment.
Question 1 (4): Consider an error correction code which generates codewords by simply re
peating each information symbol five times.
(a) What is the code rate?
(b) How many codewords are in the code?
(c) What is the minimum distance of the code?
(d) What fraction of all possible codewords are used in the code?
Question 2 (3): Consider the code of Table 1. Calculate the number of codewords with Ham
ming weight
w
= 0, 1,.
.., 7. Calculate the Hamming distance
d
between each codeword and
codeword 1111111. Compare the number of codewords with Hamming weight w = 0, 1,.
..,
7 with the number of codewords with Hamming distance
d
from 1111111.
Table 1: Typical Block Code
Message
Number
Message
Codeword
0
0000
0000000
1
0001
1100001
2
0010
0110010
3
0011
1010011
4
0100
1110100
5
0101
0010101
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 Spring '10
 Rejaei
 Electromagnet

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