EECS 373 Homework. Winter 2009
Name: _______________________________ unique name: ________________
You are to turn in this sheet as a cover page for your assignment. The rest of the
assignment should be stapled to this page. See the website for details about where to turn
in your assignment. This is an individual assignment; all of the work should be your own.
Assignments that are unstapled, lack a cover sheet, or are difficult to read will lose at
least 50% of the possible points and we may not grade them at all.
This assignment is graded out of 65 points. Due Thursday April 2st in lab by 1:40pm.
1. Consider the following error correction scheme. Bits A, B, C and D are data. Bits X,Y
and Z are error correction, where:
• X=P(A,C,D)
• Y=P(B,C,D)
• Z=P(A,B,D)
Assuming the function P(…) is the even one’s parity of the bits (that is the output
would make the number of ones even if it were concatenated to the input) answer the
following questions:
a. What would be the values of X, Y and Z if ABCD=1001) [2]
b. What correction, if any, would occur (in data or parity) if the string received
were ABCDXYZ=(0000101) [3]
c. hat correction, if any, would occur (in data or parity) if the string received
were ABCDXYZ=(1110111) [3]
d. What correction, if any, would occur (in data or parity) if the string received
were ABCDXYZ=(0011000) [3]
e. Draw gates which produce the corrected value of bit “C” given the string
received string ABCDXYZ. (Hint: lots of XOR or XNOR gates) [9]
2. Consider a new recovery scheme which can correct one bit of error over 10 data bits.
a. What is the minimum number of error-correction bits that will be needed?
Show your work. [3]
b. What is the minimum Hamming distance between legal instances of the code?
How would your answer change if we wished to provide two bits of error
correction? [5]
c. Using the “P” function described above, provide a definition for all of your
error correction bits. Use the same notation as above, with your data bits being
A,B,C etc. [6]
3. Using the Viterbi algorithm as described in class, consider the following data being
received:
Data 0
1
1
0
0
0
0
Parity
0
1
1
0
1
1
1
Show a table/chart similar to the one drawn in class and indicate what data the
algorithm indicates was sent. [15]
