p.1 of 2
Course: 71203
Module: E&T2760 Data Communications
Assignment: #3
Deadline: 25th February, 2003
Exam. 2000/2001
Q1.
An information consists of 4 bits, say k1=1,k2=1,k3=0 and k4=0 is to be
transmitted using the Hamming (7,4) code.
a) write down the three check equations and determine the transmitted code
word
b) determine the check matrix, H
c) if an error occurs in bit 3 during transmission, determine how the syndrome
may be used to correct the error
Exam. 2001/2002
Q2.
The generator matrix of the Hamming (7,4) code is shown below.
1 0 0 0 1 1 0
0 1 0 0 1 0 1

G
0 0 1 0 0 1 1


0 0 0 1 1 1 1 
a) Determine:
(i) the minimum distance of this code
(ii) the maximum number of error bits that can be detected
(iii) the maximum number of error bits that can be corrected
(iv) the check equations
b) Determine the code word for information bits k1=1,k2=1,k3=0 and k4=0
c) Determine the check matrix H.
d) If an error occurs at k3 during transmission, determine the syndrome.
e) Briefly describe how the receiver can determine the position of the error by
using the syndrome.
p.2 of 2
Exam. 2000/2001
Q3.
A (15,9) cyclic code has a generator polynomial G(x) = x6 + x5 + x4 + x3 + 1.
Information bit sequence 101010101 is to be coded and transmitted by this cyclic
code. Determine :
a) the transmitted code word
b) the remainder obtained at the receiver if an error occurs in the 7th bit
Exam. 2000/2001
Q4.
A long-distance half-duplex R.F. link uses stop-and-wait ARQ strategy and has
the following characteristics :
 Data transmission rate : 96kbps
 Frame size : 1023 bits
 Information bits per frame : 893
 Propagation delay : 15ms
 Acknowledgement size : 24 bits
 Processing delay : 4ms
 Bit error rate : 4 x 10-4
a) Calculate the frame error rate.
b) What is the average number of times that a frame is transmitted?
c) Determine the throughput rate.
Exam. 2001/2002
Q5.
A long-distance. Half-duplex radio link using stop-and-wait ARQ strategy has the
following transmission characteristics:
 frame size = 2048 bits
 information bits within a frame = 2000 bits
 data transmission rate = 9600 bps
 one-way propagation delay = 20ms
 acknowledgement transmission time = negligible
 processing delay = negligible
 bit error rate = 3*10-4
a) Calculate the frame error probability, in two significant digits.
b) Calculate the average number of times that a frame is transmitted.
c) Calculate the throughput.
--- End ---