ECE 4415/6035 – Introduction to Computer Networks Spring 2021 Homework 3

ECE 4415/6035 – Introduction to Computer Networks

Spring 2021

Homework 3

Assigned:   2/22/’21

Due:   3/1/’21

Prof. Suresh Subramaniam

Total points:   40

Reading Assignment:   Sections 4.1-4.4, 4.7-4.8

1. (5 points) If 8 bits are transmitted from a sender to a receiver, what is the probability that: (a) there are no errors in the transmission, and (b) there are either 2 or 3 errors in the transmission. Assume p is the probability of bit error.

2. (10 points) A basic error control code is the repetition code. In this coding technique, each bit is repeated an odd number of times r. For instance, if the information bit string is 0110 and r = 3, the transmitted codeword is 000111111000, i.e., each bit is repeated 3 times. The receiver uses majority logic to decode the codeword, i.e., it looks at the 3 codeword bits representing a single information bit and decides a 0(1) if the majority of the 3 bits are 0(1).

a) For the example, above, what is the decoded information if the received word is 101110111001? Explain your answer.

a. For a 4-bit information string and r = 3, what is the probability that an error will go undetected if the bit error probability is p.

3. (5 points) A baseband channel has a bandwidth of 10 MHz. What is the maximum bit rate that can be supported by bipolar line code and Manchester line code? Hint: Look at the spectrum of the two line codes in the slide presented in class.

4. (10 points) Consider a two-dimensional parity code used for (4x4 =) 16 information bits. Give (a) two examples each of a 4-bit error that is not detectable and is detectable. Also give one example each of a 6-bit error pattern that is not detectable and is detectable.

5. (10 points) Find the Internet checksum of the following four 16-bit words represented in hexadecimal (each hexadecimal digit stands for 4 bits): ACD7, B9AF, ABBA, and BABA.