Error Control Coding Asssignment 4
Due 11:00 am Friday 3 June 2011
Value in brackets indicates marks for each question. Total value of marks is 20. This assignment
counts towards 12.5% of the total assessment.
Question 1 (6): A (15,11) cyclic code has the generator polynomial
g
(
X
) = 1+
X
+
X
4
.
(a) Show that this code does not have any code words of weight 1 or 2.
(b) Show that there are at least 30 code words of weight 3. (Hint: use
g
(
X
) and
g
(
X
)
2
.)
(c) Devise a systematic encoder for this code.
(d) Devise a Meggitt decoder for this code.
Question 2 (4): We have the generator polynomial
g
(
X
)
+
1
)
X
2
)
X
4
)
X
6
)
X
7
)
X
10
(a) Show that
g
(
X
) generates a (21,11) cycle code.
(b) Devise a syndrome computation circuit for this code.
(b) Let
r
(
X
)
+
1
)
X
5
)
X
17
be a received polynomial. Compute the syndrome of
r
(
X
). Display
the contents of the syndrome register after each digit of
r
has been shifted into the syndrome com
putation circuit.
Question 3 (4): Let
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '10
 Rejaei
 Electromagnet, Coding theory, Error detection and correction, syndrome computation circuit

Click to edit the document details