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.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 email@example.com 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