ECE/CS 438  Communication Networks
Fall 2008

Homework 1
Assigned on September 3
Due by class time on September 12, 2008

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Problem numbers below refer to 3rd and 4th edition of the textbook
by Peterson and Davie.
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(1) Chapter 1 - Problem 15, parts (a) and (b) 

(2) Chapter 1 - Problem 22 parts (a) and (b)

(3) Chapter 2 - Problem 18 parts (a) and (b) 

(4) Consider messages of size 8 bits. With the addition of an even parity
    bit, it is possible to detect odd number of bit errors in the encoded message.
    The encoded message includes 9 bits, consisting of the unencoded 8-bit
    message and 1 redundant (parity) bit.

    Suppose that each bit in the encoded message can become erroneous
    (independent of other bits) with probability 0.1.
    Determine the probability that the received message will contain an even
    number of errors (and thus, the errors will not be detected). 

(5) Consider a message of size 8 bits. It is not possible add 2 redundant bits such
    that all 1-bit and 2-bit errors can be detected in any encoded message.
    Explain why.   

	Hint: To be able to detect 2-bit errors, a 2-bit error should not
              change an encoded message into another error-free message.
              Equivalently, two encoded messages, each containing a 1-bit
               error, should not become identical.

(6) Networking utilities ping and traceroute

    (a) The Unix utility "ping" can be used to estimate the round
	trip time (RTT) to various internet hosts. See the manual ("man")
	pages for ping to see how to use ping. Upon interrupting execution
	of ping, the minimum, average, and maximum RTT will be displayed.
	Report the average round trip times (over at least 5 pings) for
	uiuc.edu, berkeley.edu and www.tu-berlin.de.

    (b) The Unix utility traceroute can be used to determine route to
	a specified host on the internet. Read the man page for traceroute
	to understand its functionality. Try traceroute www.tu-berlin.de.
	How many routers are encountered along the way? Report the 9th router
	encountered for the traceroute for www.tu-berlin.de. Also, ping that router
	and compare the round trip times reported by ping and traceroute (are
	they similar?)