IT010 603 (Pages : 3) Reg.

No _______________
Name _________________
B.TECH DEGREE EXAMINATION
!"#$ emes#e%
B%a&'$: I&(o%ma#!o& Te'$&o)og*
IT 010 603 + IN,ORMATION THEOR- AND CODING
(Model Question Paper-1)
T!me: T$%ee Ho.%s Ma"!m.m : 100 Ma%/s
Pa%# 0 A
Answer all questions.
Each question carries 3 marks
1. Relate the amount of information provided and probability of occurrence of events.
2. What is the channel capacity of a binary symmetric channel ith error probability !.!1"
#. $efine the terms codin% efficiency and redundancy.
&. What is source codin%" $efine code len%th ' code efficiency. (ive the relation beteen it.
). What is meant by stop-and-ait *RQ" +,plain.
(1 2 3 3 11 ma%/s)
Pa%# 0 B
Answer all questions.
Each question carries 5 marks
-. * discrete source emits one of five symbols once every milliseconds ith probabilities
1.2/ 1.&/ 1.0/ 1.1- and 1.1-. 1ind the source entropy and information rate.
2. 3tate and e,plain 3hannon 4artley theorem.
0. $efine ( and 4 matri, and sho that ( . 4
5
6 !.
7. 8ame anyone codin% method used for burst error correction. +,plain.
1!. What is interleavin%" +,plain about bloc9 interleavin%.

(1 2 1 3 41 ma%/s)
PART 0 C
Answer any one full question from each module.
Each question carries 12 marks
11. :onsider that to sources emit messa%es ,l/ ,2/ ,# and y1/ y2/ y# ith the ;oint probabilities
p (X, Y) as shon in the matri, form<

(i) :alculate the entropies of = and >. (& mar9s)
(ii) :alculate the ;oint and conditional entropies/ 4 (=/>)/ 4 (=.>)/ 4(>.=)
beteen = and >. (- mar9s)
(iii) :alculate the avera%e mutual information ?(=@>). (2 mar9s)
Or
12. (a) $efine (i) $iscrete entropy 4 (=) and ;oint entropy 4 (=/>) and
(ii) Mutual information ?(=@>). (- mar9s)
(b) 3ho that ? (=@>) 6 4 (=)A 4 (>) - 4 (=/>). (- mar9s)
1#. $erive an e,pression for the capacity of a band-limited *W(8 channel
Or
1&. * B3: has the error probability p 6 !.2 and the input to the channel consists of &
eCuiprobable messa%es ,l 6 !!! @ ,2 6 !!1 @ ,# 6 !11 @ ,& 6 111. :alculate
(a) p(!) and p (1) at the input@
(b) +fficiency of the code@
(c) :hannel capacity.
1). * Memory less source emits si, messa%es ith probabilities D!.&/ !.2/ !.2/ !.1/ !.1E. 1ind
the 3hannon - 1ano code and determine its efficiency.
Or
1-. :onstruct the 4uffman code ith minimum code variance for the folloin% probabilities
and also determine the code variance and code efficiency<
D!.2)/ !.2). !.12)/ !.12)/ !.12)/ !.!-2)/ !.!-2)E
12. :onsider a (-/#) linear bloc9 code hose %enerator matri, is %iven by
(i) 1ind the parity chec9 matri,. (2 mar9s)
(ii) 1ind the minimum distance of the code. (& mar9s)
(iii) $ra the encoder and syndrome computation circuit. (- mar9s)

Or
10. * (2/ &) cyclic code has a %enerator polynomial< %(=) 6 =
#
A = A 1.
(i) $ra the bloc9 dia%ram of encoder and syndrome calculator.
(ii) 1ind %enerator and parity chec9 matrices in systematic form.
17. (a) +,plain the or9in% of (2/1/#) convolutional encoder usin% transform
domain approach. (- mar9s)
(b) +,plain 3eCuential decodin%. (- mar9s)
Or
2!. (a) +,plain the ma,imum li9elihood decodin% and viterbi decodin% al%orithms of a
convolution encoder. (0 mar9s)
(b) $escribe about bloc9 and :onvolutional interleavin%. (& mar9s)

(1 2 14 3 60 ma%/s)
IT010 603 (Pages : 3) Reg. No _______________
Name _________________
B.TECH DEGREE EXAMINATION
!"#$ emes#e%
B%a&'$: I&(o%ma#!o& Te'$&o)og*
IT 010 603 + IN,ORMATION THEOR- AND CODING
(Model Question Paper-2)
T!me: T$%ee Ho.%s Ma"!m.m : 100 Ma%/s
Pa%# 0 A
Answer all questions.
Each question carries 3 marks
1. $efine (i) Foint entropy@ and (ii) :onditional entropy.
2. 39etch the transition dia%ram of a binary erasure channel and e,plain.
#. What are instantaneous codes"
&. 1ind the %enerator and parity chec9 matrices of a (2/ &) cyclic code ith %enerator
polynomial % (=) 6 1 A = A =
#
.
). What is meant by constraint len%th and free distance of a convolution code"
(1 2 3 3 11 ma%/s)
Pa%# 0 B
Answer all questions.
Each question carries 5 marks
-. $efine Mutual ?nformation. +,plain ho it is related to entropy for a lossless channel/ prove
that 4(=.>) 6 !.
2. (ive the relation beteen channel capacity :/ bandidth W and si%nal to noise ratio 3.8 of
a *W(8 channel. +,plain the trade-off beteen them.
0. $efine B:4 code and brief about Reed-3olomon code.
7. +,plain briefly the syndrome calculation circuit for (n/9) cyclic code.
1!. Briefly describe the steps of Giterbi al%orithm.
(1 2 1 3 41 ma%/s)
PART 0 C
Answer any one full question from each module.
Each question carries 12 marks
11. (a) Prove that the entropy for a discrete source is ma,imum hen the output symbols are
eCually probable.
(b) 1ind the discrete entropy for the source ith symbol probabilities
D!.#/ !.2)/ !.2/ !.1)/ !.1E
Or
12. (a) $efine mutual information ? (= @ >) and sho that ? (= @ >) H !.
(b) $erive the relationship beteen entropy and mutual information.
1#. (a) 1rom channel capacity theorem/ find the capacity of a channel ith infinite
bandidth and e,plain. (- mar9s)
(b) 5o binary symmetric channel ith error probability !.1/ are cascaded as shon
belo and P (!) 6 !.2).:alculate ? (=/>)and ? (=/I).
(- mar9s)
>
= I
Or
1&. (a) 3tate 3hannon-4artley theorem and from that derive 3hannonJs theoretical limit.
(2 mar9s)
(b) What is meant by optimum modulation system" +,plain. () mar9s)
1). (a) 3tate and prove KraftJs ineCuality. (2 mar9s)
(b) +,plain about arithmetic codin%. () mar9s)
Or
1-. (a)(iven ,i6D,1/ ,2/ ,#/ ,&/ ,)/ ,-Eith probabilities p(,i)6 D!.#/ !.2)/ !.2/ !.12/ !.!0/ !.!)E.
Ma9e 4uffman code. 1ind efficiency of this code. (0 mar9s)
(b) What is I?P codin%" +,plain. (& mar9s)
B3:-1 B3:-2
12. (a) +,plain the encodin% method of a (2/ &) linear bloc9 code. (- mar9s)
(b) $efine %enerator and parity chec9 matrices of a (2/ &) linear bloc9 code. +,plain ho
to %enerate a linear bloc9 code usin% (-matri,. +,plain ith an e,ample. (- mar9s)
Or
10. :onstruct a symmetric (2/&) cyclic code usin% the %enerator polynomial %(,)6 ,
#
A,A1.
What are the error correctin% capabilities of this code" 1or the received ord 11!11!!/
determine the transmitted codeord.
17. :onsider (#/1/2) convolutional code ith %(1) 6 (11!)/ %(2) 6 (1!1) and %(#) 6 (111)<
(i) $ra the encoder bloc9 dia%ram.
(ii) 1ind the %enerator matri,.
(iii) 1ind the code ord correspondin% to the information seCuence (111!1)
usin% time domain approach.
Or
2!. +,plain *RQ in detail.
(1 2 14 3 60 ma%/s)