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Hw2_001

# Hw2_001 - ECE 5670 Digital Communications(Spring 2011...

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ECE 5670 : Digital Communications (Spring 2011) Homework 2 Due February 10 in class Instructor: Salman Avestimehr Oﬃce 325 Rhodes Hall 1. Suppose we are employing sequential communication to work at data rate R bits per unit time and error probability p e . In Lecture 2, we saw that doubling the transmit energy allowed us to either approximately: increase the data rate by 0.5 bits per unit time or improve the reliability by making the error probability equal to p 2 e . Suppose than an engineer wants to increase the data rate and increase reliability at the same time, while still only doubling the transmit energy. The improvements are as follows: data rate is now R + r bits per unit time and error probability is now p d e . Calculate the entire set of values ( r, d ) can take. Based on our earlier observation, this set should include the points (0.5,1) and (0,2). 2. In this exercise we see the tradeoff between data rate and SNR while communicating reliably at certain desired level using the sequential communication scheme.

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