Exam in TNE066 Telecommunications – Practice Test

Exam in TNE066 Telecommunications – Practice Test
It is permitted to bring and use the following materials:
Pocket calculator
English dictionary
Formula sheet – one paper of A4 size with handwritten formulas (it must not
contain any examples, solutions or other text than formulas with short
descriptions of the variables)
The exam consists of 6 problems and it is possible to get at most 30 points.
The grade limits are:
Grade 3: 15 points
Grade 4: 21 points
Grade 5: 27 points
Write clearly and properly. Answers that are unreasonable, unreadable or not
understandable will not yield any points.
Good luck!
1. Is each of the following statements (a-j) true or false?
Each correct answer gives 1p. Each incorrect answer results in -1p.
(Note: You do not have to justify your answers. However, if you believe that a statement is in general
true but there are rare exceptions so you choose to mark the statement as false (or vice versa), please
do provide a justification.)
a) Kraft’s inequality tells us whether it is possible to construct a tree code for a given
set of codeword lengths.
b) An error correcting code has the code rate 0.25, this means that 25 % percent of
the codeword bits are parity/redundant bits.
c) Fading is desired in wireless communications as it increases the communication
performance.
d) In order to avoid that two sources transmit at the same time, guard intervals are
typically used in TDMA? (1p)
e) If s = H·r T = 0 in error control coding (where r is the received codeword), this
means that the received codeword is not a valid codeword.
f) Thermal noise is only present in wireless communications.

g) Quantization is performed to obtain a digital representation of an analog signal
that has been sampled.
h) The strategy of the OOK modulation technique is to represent digital data as the
presence or absence of a carrier wave.
i) Soft decision decoding typically results in greater performance compared to hard
decision decoding.
j) The Go-back-N ARQ technique is restricted to only send one single data packet
at a time, and an acknowledgement needs to be received before the next packet may
be transmitted.
2. A signal x(t) = sin(500πt) is sampled and then reconstructed ideally. Determine the
output y(t) after ideal reconstruction if the sampling frequency f s is:
a) f s = 600 Hz. (2p)
b) f s = 300 Hz. (2p)
3. A step-index fiber is surrounded by air. The cladding has refraction index 1.2 and the
core has refraction index 1.4.
a) Determine the angle of refraction if the light in the core reaches the junction
between the core and the cladding with an angle of incidence that is 40 o . (1p)
b) Determine the critical angle of the core/cladding junction. (1p)
c) Determine the acceptance half angle of the fiber. (1p)
d) Briefly describe two types of losses that are associated with optical fiber. (1p)
4. A memoryless source produces the symbols A, B, C, D, E, F, G, H with the
probabilities P A = 0.28, P B = 0.20, P C = 0.15, P D = 0.06, P E = 0.18, P F = 0.05, P G
= 0.07, P H = 0.01.
a) Determine the average codeword length that can be achieved with a tree code
(Huffman code) which encodes one symbol at a time. (2p)
b) Calculate the compression ratio and the redundancy. (2p)

5. a) Create the generator matrix G and the parity check matrix H for a linear error
correcting block code with the parameters (n, k, d) = (8, 2, 4). (2p)
b) How many errors can the code detect and correct? (2p)
6. The minimum Euclidean distance d between symbols in a signal space diagram is
often used as a quality measure for data transmission systems. Sometimes the
normalized distance
d
is used instead, where E is either the maximum or
E
average energy of the signal constellation.
Since d depends on the energy E of the signals, determine the value of the
normalized minimum distance for 16-PSK and 16-QAM when:
a) E corresponds to the maximum energy of the constellation. (2p)
b) E corresponds to the average energy of the constellation. (2p)
Hint: The symbol error probability of 16-PSK can also be written as:
P e
2 Q
d
2
2 N
0