EE 421 – Fall 2010  Midterm A
Answer as many questions as you can out of the following:
1) Consider the binary code composed of the 4 codewords:
C
1
={(0000000),( 1100110),( 0011001), (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
200 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
200 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).
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '11
 Mondin
 Coding theory, Hamming Code, Minimum distance, parity check, parity check matrix

Click to edit the document details