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# ex6 - CS70 Discrete Mathematics for Computer Science Spring...

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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. Error-correcting codes (a) Recall from class (Lecture Note 8) the error-correcting 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. Error-correcting codes: An example In this question we will go through an example of error-correcting codes with general errors. Since we will

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ex6 - CS70 Discrete Mathematics for Computer Science Spring...

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