Problem set 6 (Tuesday 4.12.2001)

1. Nyquist and Shannon
   1. What is the content of the theorems of Nyquist and Shannon? How do these theorems relate to each other?
   2. Television channels are 6 MHz wide. How many bits/sec can be sent if four-level digital signals are used? Assume a noiseless channel.
   3. A noiseless 4-lHz channel is sampled every 1 msec. What is the maximum data rate?
   4. A binary signal (getting only values 0 and 1) is sent over a 3 kHz channel whose noise-to signal ratio is 20dB, what is the maximum achievable data rate?

2. T1 and SONET
   1. If a T1 carrier system slips and loses track where it is, it tries to resynchronize using the 1st bit in each frame. How many frames will have to be inspected on the average to resynchronize with a probability of 0.001 of being wrong?
   2. SONET clocks are pretty exact and their timings are drifting apart only about 3 seconds in 100 years (a year = 365 days). How long does it take before the drift between two SONET clocks is equal to the width of 1 bit? What are the implications of this calculation in practice?

3. About modems
   1. How is a V.90 standard modem functioning? How is it possible to achieve 56 kbps rates, though the theoretical maximum for telephone network is only 35 kbps? And why is it only 56 kbps and not 64 kbps?
   2. A modem modulates digital bits first into analog form so that they can be transmitted in the analog local loop and at the receivers the modem demodulates the analog signal back to the digital bits. A codec samples the analog signal and encodes the samples into digital bits and at the other end the codec decodes the digital signals back to analog. How does the coding side of codec differ from the demodulation side of the modem or is the no difference at all? Both transform an analog signal to a digital one.

4. Token bucket
   1. An ATM networks uses a token bucket scheme for traffic shaping. A new token is put into the bucket every 5 microsecond. What is the maximun sustainable net data rate (i.e., excluding header bits)?
   2. A computer on a 6-Mbps network is regulated by a token bucket. The token bucket is filled at a rate of 1 Mbps. It is initially filled to capacity with 8 megabits. How long can the computer transmit at the full 6 Mbps?

5. There are proposals for two different ways to add quality of service to Internet. Explain the most important features of these proposals. In your opinion which of these ways seems to be the better way to add quality of service to Internet? Is it really necessary to add any Quality of Service at all to Internet? Wouldn't it be enough just to put enough capacity and bandwidh into the lines?

6. Your opinions about this course.
   1. The content of this course has been changed quite a lot. What subjects were, in your opinion, the most interesting and important ones? What subjects were unnecessary? How should the course be changed in the future? What missing subjects should be included? What items could be dropped from the course?
   2. Fill the teaching evalution form for this course (http://ilmo.cs.helsinki.fi/kurssit/servlet/Valinta).