ELEC 471, Spring 1999
Prof. Rich Kozick

## Homework 3 -- REVISED

Date Assigned: Thursday, January 28, 1999
Date Due: Thursday, February 4, 1999

1. Exam 1 will be on Thursday, February 4. The topics will include everything that we have done in class through January 28. This includes topics in the text in Sections 1.1-1.6, as well as the digital communication application.

2. Reading: Continue studying Chapter 1, Sections 1.8 and 1.9. Also read Chapter 2 for class on February 11.

3. On February 11, we will work on a MATLAB simulation of the digital communication system that we discussed in class on January 28.

For Feburary 4, be sure that you understand the steps we used to derive the decision algorithm for the system. Also be sure that you understand how we computed the probability of a bit error. You do not have to submit anything for this item.

4. Consider the following modification to the digital communication system. 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.

Please submit a written solution for the probability of a bit error for this system on February 4.

Thank you.