Homework: 22C:178 & 055:134

Computer Communications Fall 1998

Assignment 5 [due in class 14 October]

Unlike previous homeworks, this assignment asks you to solve some traditional textbook-like problems, based on the theoretical material presented in class and in the Peterson & Davie textbook.

A certain satellite protocol uses radio waves that range between 16.64cm and 18.75cm in wavelength (i.e. approximately 6.5 inches to 7.5 inches). If we assume two-level signalling is used, what is the maximum possible bit rate for this protocol? (Note: you can visit companies such as www.ghz.com, www.verticom.com, www.comtechcom.com, www.pioneerconsulting.com, and others to actually see specifications on such satellite equipment.)
Suppose you have a 1.7MB file to send over a link of length 1900km. The link uses electrical signals that travel at 200,000,000 meters per second. Our goal is to have a link that will have a small total delay to transfer the file from one end to the other, so we need large bandwidth. The ``link factory'' can manufacture this link with any desired bandwidth. However, we know that (a) larger bandwidth is more expensive, and (b) increases in bandwidth eventually don't reduce delay by very much. To illustrate point (b), what is the smallest bandwidth T so that a bandwidth of 2T would reduce the total delay no more than 5%?
Which gives the higher data rate, doubling the bandwidth of frequencies used to encode a signal, or doubling the power of the transmitter? (Assume noise remains the same in either case.)
The textbook points out that it is possible for the bit rate of a data link to actually exceed the signal rate (baud rate), simply by encoding bits with more than two levels of signal. Suppose instead of using two discrete signal levels, we want to have higher data rate and so propose 16 signal levels. In order to use 16 levels, it is necessary to have far more precision in the circuitry that samples frequencies (this is equivalent to using more terms in the Fourier expansion -- we are using more ``harmonics''). If this extra precision requires 5 times the bandwidth than a two-level signal would require, is our proposed encoding worthwhile?
Note: This question is poorly stated, and therefore could be legitimately answered either way. Certainly, if you can use sixteen level encoding, it carries more information than two-level encoding and if we compare the two -- even at 5 times the original bandwidth -- the sixteen level encoding always is worthwhile. However, there is another interpretation, more in the spirit of engineering. Suppose that in order to use sixteen level encoding, one must arrange for two "empty bands" on either side of the intended signalling band. For instance, here are the two scenarios:

     |       |       |       |       |       |
     |       |       | used  |       |       |
     |       |       |  for  |       |       |
     |       |       |   16  |       |       |
     |       |       | level |       |       |
     |       |       |       |       |       |

According to this picture, a total of 5H channel bandwidth is set aside to permit a maximum bit rate (by the Nyquist limit) of 8H bits per second. But if we suppose that the entire 5H could be used safely with two level encoding, then we could get 10H bits per second.

Suppose we have a baseband link that uses NRZI with 4B/5B encoding, and the HDLC framing protocol with an average of 1KB of user data per frame generated on the link. The link uses two-level encoding of the baseband signal, simply alternating between the two levels for the NRZI encoding. The maximum signal rate on the link is 1/16 the maximum Hz frequency allowed on the link, and this maximum is 100MHz. (In other words, at the maximum signal rate, there would be about sixteen ``waves'' of the highest harmonic per bit of signalling.) What is the link's throughput (i.e. what is the effective bandwidth) considering all the factors of encoding and framing?

Turning in your answers:

You can submit your homework using email, but this may not be advisable: there will be calculations in your answers and for the grader to give partial credit and proper feedback on your answers, you may better turn in your homework on paper -- in class on 14 October or via fax (attn: Ted Herman, fax number (319) 335-3624.

However you submit your answers, remember to write your four-digit ID number (the last four digits of your student ID), the words Homework 5 and the class name 22C178 (or 055:134).

If you choose to use email to answer the questions, follow the normal instructions, namely mail the homework to herman@cs.uiowa.edu and specify in the subject line, the course number, the assignment number and the last four digits of your student ID number. So, for example if your student number is 123456789, then the subject line of your email should be:

178 homework 5, student 6789
If you do not have such a subject line, I will bounce your letter back to you and ask for a resubmission of the homework.

Ted Herman