ELEC 471, Spring 2001
Prof. Rich Kozick

## Homework 3

Date Assigned: Tuesday, February 6, 2001
Date Due: Thursday, February 8, 2001

1. Reading: Continue studying Chapter 1, particularly Sections 1.7, 1.8, and 1.9.

2. Please solve the following problems at the end of Chapter 1, and submit your solutions on February 8:
1.7.1
1.7.3
1.7.5
1.7.6

We will not have a short quiz on February 8.

3. Study the digital communication application discussed in class. Be sure that you understand the steps we used to derive the decision algorithm and the probability of a bit error for the system. You do not have to submit anything for this item.

4. As you read Section 1.9, consider the following modification to the digital communication system. You do not have to submit anything yet, but you will need to answer this as part of Homework 4, which will be assigned on February 8.

Suppose that each bit is transmitted three times, with independent noise added on each transmission. Make your "overall" decision for each bit as the majority of the three individual decisions. What is the probability of a bit error for this system? For some hints on the analysis of this system, refer to Section 1.9, and Example 1.36 in particular. Or, you can just look at the sample space of repeating the experiment three independent times. What are the probabilities of the outcomes in this sample space? Which outcomes correspond to an error? From this, you should be able to compute the probability of an error.

Thank you.