USN Time: 10EC55 (06 Marks) (04 Marks) Marks) Marks) Fifth Semester B.E. Degree Examination, Dec.2013 /Jan.2O14 lnformation Theory and Goding 3 hrs. Note: Answer FIVEfull questions, selecting at least TWO questions from eoch part. PART _ A Define: i) Unit of information, ii) Entropy, iii) Information rate. rate of the solriee. c. Find Gr and Gz and verify that Gr > G2 > H(s). ?u= z/rt Fig.Q1(c) Y):H(X/Y)+H(Y). Max. Marks:10O ... 'l c) o o g o o ! oX dv ! -^l troo .-r .= .\ i: o0 tso otr -o =P o2 a= oO 6O boi -o so -a .) 6 .!J i9 o." oj 6: G; !o >'h lo0 so tr> =o 5L U< - c'i a.) o Z o la. b. The output of an information source consists of 128 symbols 16 of which occur with a probability of ll32 and remaining occurs with a probability of !22! The source emits 1000 symbolslsee assuming that symbols are chosen independently. Find the average information Show that H(X, Apply Sha nco ding algorithm. iofu f,o llowing message : nnon encodlns a Symbols Sr Sz Si Probabilities 0.5 0.3 0.2 i) Find the code efficiency and redundancy. il) If the same technique is applied to the second order extension of the source, how much will the redundancy be improved. (10 Marks) A technique used in a source encoder is to arrange message in a order of decreasing probability, divide message into two almost equal groups. Message in 1" group are assigned zero. Messages in 2nd group are assigned with 1. Procedure'is repeated till no further 3a. b. division iq,po;sible. Find code words for 6 messages. State the properties of mutual information. ..... (06 Marks) State S-hannon's Hartley law and its implifications. ,:::,,:, (05 Marks) Apply Huffman coding procedure for the following set of messages and determine the efficiency of the binary code so formed symbols Xr, Xz, X: with probadilities 0.7, 0.15, 0.15. If the same technique is applied to the 2nd order extension for the above messages. How much will the efficiency be improved? (10 Marks) For an AWGN channel with 4 kHz-B.W and noise spectral density No/2 : 10-t2 WHz. The signal power required at the receiver is 0.1 mW. Calculate the capacity of the channel. (05 Marks) (04 Marks) For the JPM given below, compute individually H(X), H(Y), H(X, Y), H(Y/X), H(X/Y) and I(X, Y). Verify the relationship among these entropies. lo.os o o.2o o.osl l n o.ro oro o l PtX.Yt:l I | 0 0 0.20 0.r0| 10.0s 0.0s 0 0. r0_l c. (10 Marks) For More Question Papers Visit - www.pediawikiblog.com For More Question Papers Visit - www.pediawikiblog.com www.pediawikiblog.com
Welcome message from author
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
USN
Time:
10EC55
(06 Marks)
(04 Marks)
Marks)
Marks)
Fifth Semester B.E. Degree Examination, Dec.2013 /Jan.2O14
lnformation Theory and Goding
3 hrs.Note: Answer FIVEfull questions, selecting
at least TWO questions from eoch part.
PART _ ADefine: i) Unit of information, ii) Entropy, iii) Information rate.
rate of the solriee.c. Find Gr and Gz and verify that Gr > G2 > H(s).
?u= z/rt
Fig.Q1(c)
Y):H(X/Y)+H(Y).
Max. Marks:10O
... 'l
c)oog
oo!
oX
dv!-^ltroo.-r.= .\i: o0tsootr-o
=P
o2
a=
oO6O
boi
-o so
-a .)
6 .!J
i9o."oj
6:
G;!o
>'hlo0
sotr>=o5L
U<- c'i
a.)
oZ
o
la.b. The output of an information source consists of 128 symbols 16 of which occur with a
probability of ll32 and remaining occurs with a probability of !22! The source emits 1000
symbolslsee assuming that symbols are chosen independently. Find the average information
Show that H(X,Apply Sha nco ding algorithm. iofu f,o llowing message :nnon encodlns a
Symbols Sr Sz SiProbabilities 0.5 0.3 0.2
i) Find the code efficiency and redundancy.il) If the same technique is applied to the second order extension of the source, how much
will the redundancy be improved. (10 Marks)
A technique used in a source encoder is to arrange message in a order of decreasingprobability, divide message into two almost equal groups. Message in 1" group are assigned
zero. Messages in 2nd group are assigned with 1. Procedure'is repeated till no further
3a.b.
division iq,po;sible. Find code words for 6 messages.
State the properties of mutual information.
.....(06 Marks)
State S-hannon's Hartley law and its implifications. ,:::,,:, (05 Marks)
Apply Huffman coding procedure for the following set of messages and determine theefficiency of the binary code so formed symbols Xr, Xz, X: with probadilities 0.7, 0.15,0.15. If the same technique is applied to the 2nd order extension for the above messages.
How much will the efficiency be improved? (10 Marks)For an AWGN channel with 4 kHz-B.W and noise spectral density No/2 : 10-t2 WHz. Thesignal power required at the receiver is 0.1 mW. Calculate the capacity of the channel.
(05 Marks)
(04 Marks)For the JPM given below, compute individually H(X), H(Y), H(X, Y), H(Y/X), H(X/Y) andI(X, Y). Verify the relationship among these entropies.
lo.os o o.2o o.osl
l n o.ro oro o lPtX.Yt:l I
| 0 0 0.20 0.r0|
10.0s 0.0s 0 0. r0_l
c.
(10 Marks)
For More Question Papers Visit - www.pediawikiblog.com
For More Question Papers Visit - www.pediawikiblog.com
www.pediawikiblog.com
4 c. The noise characteristics shown in Fig.Q4(c), find channel capacity.
10EC55
(06 Marks)
(06 Marks)
by listing the(10 Marks)
K1
Ny
Y,
\-
5a.b.
, Fig.Qa(c)
: PART_B
What are the different methods of controlling errors? Explain.For a systematic (7, 4) linear code, parity code is given by
P_
Find all possible vatii cile vectors.Draw the corresponding on0oding circuit.A single error has occurred in'bach of thesb vectors detect and correct these errors:
YA: [0111110], Ye: [101I100], Yc: [1010000]Draw the syndrome calculation circuit. (14 Marks)
t, ,,' I
1,1 0
l01,011
a. What is binary cyclic code? Describe the features of encoder and decoder used for cycliccodes using an (n - k) bit shift register. (10 Marks)
b. Consider(15, 11)cyclic codesgenerated byg(x) : I +x +x4:i) Device a feedback re$ister encoder for this code, .
ii) Illustrate the encoiling procedure with the message vector 11001101011states of the register.
Write explanatory note on:a. RS codes
b. Golay codesc. Shorterld cyclic codes
d. Buist Error Correcting Codes
''-'' Consider (3, 1, 2) convolutional code with impulse respons. gt') :,r:):1lll).i) Draw the encoder block diagram.ii) Find the generator matrix.iii) Find the code vector corresponding to
transform do main approach.
(20 Marks)
(110), g{2) = (101),8
"l:... '
message sequence 11101 using time domain and(20 Marks)
2 of2For More Question Papers Visit - www.pediawikiblog.com
For More Question Papers Visit - www.pediawikiblog.com
www.pediawikiblog.com
Related Documents
