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EE 421 – Fall 2010  Midterm B
Answer as many questions as you can out of the following:
1) Consider the binary code composed of the 4 codewords:
C
1
={(0000000),(0110011),(1001100), (1111111)}
•
Is this code linear? Which are its n
1
and k
1
values?
•
What is its minimum distance d
min1
?
•
Select a basis for C
1
and find its H and G matrices.
•
Which are its correction capabilities
t
1
and detection capability
e
1
?
•
Which is the distance spectrum of the code?
•
If the encoder for C
1
receives an input bitrate of R
in
370 kbit/s, which is the output bitrate R
out
on the channel?
•
Generate the associated
extended
code C
2
by adding one parity check equation to the H matrix
containing only “ones”(and the corresponding column with all “zeros” and one “one”). Write
the parity check matrix H
ext
of C
2
.
•
Which are the n
2
and k
2
values for C
2
?
•
If the encoder for C
2
receives an input bitrate of R
in
370 kbit/s, which is the output bitrate R
out
on the channel?
•
What is its minimum distance d
min2
of C
2
?
•
Find a possible basis for C
2
(combination of the rows of H
ext
and permutation of the columns
are allowed, equivalent codes are allowed).
•
Find the correction capability
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 Spring '11
 Mondin

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