CS70 Discrete Mathematics for Computer Science, Spring 2012
Homework 6
Out: 1 March. Due: 5 pm, 8 March.
Instructions:
Start each problem on a new sheet. Write your name,
section number
and “CS70” on every sheet.
If you use more than one sheet for a problem, staple them together (but do
not
staple different problems together).
Put your solutions in the boxes on Soda level 2 by 5pm on Thursday: your solution to Q1 goes in box CS70–1, your
solution to Q2 goes in box CS70–2, and so on (
five
boxes total). You are encouraged to form small groups (two to four
people) to work through the homework, but you
must
write up all your solutions on your own.
1. Errorcorrecting codes
(a) Recall from class (Lecture Note 8) the errorcorrecting code for erasure errors, which protects against
up to
k
lost packets by sending a total of
n
+
k
packets (where
n
is the number of packets in the
original message). Often the number of packets lost is not some fixed number
k
, but rather a
fraction
of the number of packets sent. Suppose we wish to protect against a fraction
α
of lost packets (where
0
< α <
1
). How many packets do we need to send (as a function of
n
and
α
)?
(b) Repeat part (a) for the case of general errors.
2. Errorcorrecting codes: An example
In this question we will go through an example of errorcorrecting codes with general errors. Since we will
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 Spring '08
 PAPADIMITROU
 Computer Science, Graph Theory, U.S. Census Bureau, Remote control, Bipartite graph

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