Anadolu Oniversitesi - EE Department - EEM 468 (Final) 587...Anadolu Oniversitesi - EE Department -...

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Anadolu Oniversitesi - EE Department - EEM 468 (Final) Student Name: Student Number: Questions Date: 03.06.2008, duration: 2 hours Open book exam 1. (40 Points) In the convolution encoder shown below, two bits at a time are fed to the IP. The OP is taken by rotating the indicated switch upwards as shown by the arrow. For the given configuration, determine the code rate (k / n), constrain length (L), find the generator sequences (gh g2), draw the state and trellis diagram. Assuming 1101000101 is fed to this encoder, find the output of the encoder, and at receiver side, feed this output to the trellis diagram and perform the decoding. Comment on your results IP rc~ OP Jo ILI;/~/) , i:. =- 2- f) ~ c= <1,6 rc,Je- ))/J -=- L - J )h) /lO! / e. u)o /' ! b 1,,- I) j')pv/d je..- IJ) ~ I ,) / I /c£e- ) - / for !ljt- 1°'/;> v)'- 0) fh/j j LJ~) j-, v I? IA~f) k I)l 0, f' '/ = / A.- - ..) At' [[:tv1 468 Final Exam 03.06.2008 Sa) fa 1

Transcript of Anadolu Oniversitesi - EE Department - EEM 468 (Final) 587...Anadolu Oniversitesi - EE Department -...

  • Anadolu Oniversitesi - EE Department - EEM 468 (Final)

    Student Name:Student Number:

    Questions

    Date: 03.06.2008, duration: 2 hoursOpen book exam

    1. (40 Points) In the convolution encoder shown below, two bits at a time are fed to the IP.The OP is taken by rotating the indicated switch upwards as shown by the arrow. For thegiven configuration, determine the code rate (k / n), constrain length (L), find thegenerator sequences (gh g2), draw the state and trellis diagram. Assuming 1101000101 isfed to this encoder, find the output of the encoder, and at receiver side, feed this output tothe trellis diagram and perform the decoding. Comment on your results

    IP rc~ OP

    Jo ILI;/~/) , i:. =- 2- f) ~ c=

  • / J 2-::' 1.- / / () ]

    ( J 0/0

    1/01

    1 )! .~ 1/10-'

    UJaoj -"I> L -Ie,!

    ----- /IF e /1/ J .c:rV rQ?1/1

    - ()--\

    lou

    I/o ~

    \//)1 \

    'yQ!

    :u

    \

    o

    ') 0

    /J

    Uj

  • (L q,e_ lui)tqe 1J /AoJ ~ r/o/e. I •.//O/) j/ fy all

    I/J 0/.)/

    ?6 I /D

    00

    Cj II

    C a/I ~II'U ( I r d /' /

    I(U C;)

    J)

  • ~o

    rlcD

    C'< .wu

    ----- 0E " H0l -01[j] Q)0.. -M ..c:~ .wIi1 QJ0l

    .wrl cD:> H rl>:: QJ rl0 HU GJ rl/' ,r::tJ1>:: ;?: '0-01 01 C.'d 0 f(j0 0U 01/' rl GJt- [j] [JJ

    CO -01 0 -01trI ~ 0Ii1 r.j rl C.0U H C. 'dIi1

    p" QJ -01 'd tJ1/' H , 0\° r.j

    >, ;::: tn (f] .w 'd 0 roGJ H (j) Q) I ;?: Q)2: :> 0 H "C tn E [JJ 0 rl - [JJ/'·01 l~ C. ;::: H -01 ;::: ro 'd -01Q)

    0 tn .w cD ·01 0 g H 0.w (fJ ~ 'd ~ .w cD Z0 Q) rl -01 [JJ H >4 Q) g ..c:E 'd ro ..c: -01 0 Q: ..c: 'd ..c:(j)[JJ 0 -01 [JJ ~ U P< .w 0 - .0P': H U E ro U -01 U [JJ - -MIi1 0 ;::: 0 .w 0 cD 010 3 -M U 3E--< H Q) C. C1l H ..c: c.~ H >, ..c: P< rU tn .w tn ;:J QJ/'QJ rl rl .w .w C tn C. H 'd[JJ I rU 0 ~ C11 'd -M C -01 .w 0tn

    ;::: ~ c 0.. >, 0 'd H 'd (j) 'd - IJ0 0 rU C1l 0 rl 0 - (j)-.-1 I -01 H :3 ;::: (j) ..c: u - u ;::: Q.w 0 Ll 0 0 ..c: (j) rl (j) QJ.w ;::: ::J .w GJ .w Q 'd rl 'dQJ ~I r.j ..c: .w H ..0 C(f] 0 H .w n:j (j) u 'd H .w .w ro'd 0 :> QJ .w tn 'd C. C QJ UC. C. .w 0 C. 0 ::J C11 'd QJ .w (j)c 0 0 (j) ro ;::: -01 U H C H - 'dro U tn ..c: [j] C. .w tn rU H QJ 0[JJ rl .w (j) [JJ Ii1 C H 0 [JJ U

    GJ ..c: ·01 -.-1 U • .-1.w 0 ..c: C') (j) .w EO ,10 >:: 'd + 0>:: .w Ll ..c: (j) 0 - Z (j)(j) rl [JJ 0 EO ~ W rl U (j) (j) I tnE ;::: -.-1 Z 0 0.. ..0 C. 'd [fJ ..c: rU;:J0 C H ....:J .w QJ .w Ii1 0 -.-1 .w [fJu ..c: 4-, F-< '" 'd U 0 -.-1 [fJ0 0 "C .w 0\° -..-I Z [JJ -..-I ro Zco u .w [JJ GJ -rl GJ .w c :> I -rl :> 0.. I"- II C. rl H 0l 0 r'1 ..c: ..c: E ..c:0 ~ GJ 0 rU ~ >, u p:j .w .w 0 .w0 4-< Q) C. U :> .w rl (j) -..-I U Q) -..-IN 0 t:J1 ,..-I ·rl ....:J ~ 0 (j) t:J1 Q) • .J 3 ,..; Q) - tn 3 (j)rl n:j ~ Q) ::J F-< • ..-1 0.. >:: 'd n:j '0 H 10 '0 n:j 1'00 [fJ QJ ..c: tJi

  • 2. (30 Points) Design a (5, 2) linear block code,

    a. Choose the codewords to be in systematic formb. Choose them with the aim of maximizing dmin.c. Find the generator matrixd. Find the parity check matrix

    ",t 0/ C{;; 0 n .' a) 71; ~ /' c-J ( 'II~/r)c/}I- /f /'1 f c;? Jc. I::; ,/Y) fi IIOIJ

    L /YJe:»CrJ L)D 0

    () /

    /J

    ()O 600

    0/ I 0 /

    /0 / / 0 Ci J L

  • I J

    I ) () ~JI }/\

    ~J

    I ---

    J) r- ~j10 he / Q..... f ~ / )( / 0/ 0

    0

    t I IG

    0

    ::.

    tI

    + () ~A

    f,.. I

    (, I

    --0

    I '"'{

    L

    D / 0 I D

    I 0 () 0 I

    c h ~ (..t-ry7o/r.X

    f C1 f /jJ~ hue f erC!.- - I'/ \:) 0

  • 3. (30 Points) Answer the following questions as True or False. For the False ones, givethe correct answer or the reason. For the True ones, justify the reason

    a) In cyclic codes, the generator matrix is formed by dividingpn-i by the generatorpolynomial: /.

    lIlA e loy f~II/)J J «! l... A; [...Vc.. q( JI tic

    b) Attenuation in a fibre originates from dispersion: rrr If c- / ,IJCI7Jf(I/t!:>/l //)

    c) Convolutional codes have no memory: r aIJ e / !Ac (':>1/( c; ) c:>J( yy'{) s

    I ~~/'ljCJrMt1/O/J 6/k cJe ~;rJ(/?e--I~ e. (~/l J D I\J //~/7q / e f/c '" d c>r.

    d) The cyclic property is checked by shifting the most left bit of the codeword to the end ofthe codeword: -

    / rv e-

    C(ll -L C.,2 c " Cf} C J Je) Trellis diagram is used for encoding as well as for decoding: Ir v e....

    /- I)

    A(: EEl\,f -1-68final F",am 03,C16.:::00R Sa: f~l ;

  • - .L /} 'jl!j I- ( L)7;e~j - /1tL-n/) JI'7 r1/YJ )) J '71/'1 e.-- ~J

    1'j -5 ?. 7 C>f jJr Dr, tl/.- ;)0:)2... -IV/- LJ /.J J 'Ire.. c!;J/~/}C-.

    !-//)d rJ') Ik 0;0 tJ I'fi //Jler/Ot C/;/ f

    ,

    /I

    6 I 0 ') o / ~ II,/-l/) ~ 9 d 6 r '-jt 1/.J t /:J -f- L

    I )..j- //

    () ()II I 0 cf y .3 e.-f/17 fc.r /c,('l::.....:) )

    0/) == o I /0 " 0 II OJ() / 01

    I I / 0 I I o /

    /0}

    '"

    I~L 3 q !"YL£- cc;/} 6e oJ}t:f/~c

  • Anadolu Universitesi - EE Department - EEM 468 (Final)

    Student Name:Student Number:

    Questions

    Date: 05.06.2007, duration: 2 hoursOpen book exam

    1. (40 Points) For the convolution encoder shown below, determine the code rate (k / n),constrain length (L), find the generator sequences (g), g2), draw the state and trellisdiagramme. Assuming 1101000101 is fed to this encoder, find the output of the encoder,and at recei ver side, feed this output to the trellis diagramme and perform the decoding.Comment on your results

    /

    IP c~op

  • 1/ /0 ~V

    /'

    1// (

    00/00-L0 0 ~I

    1/0/- ~-0/0/

    --

    0/ II

    0/

    l') Jo :) • -----....,.-

    \ "'-/0

    o I

    I 0

    II

    \

    IJ \

    "-\1

    -\l

    10":l •• _

    """ I 10-~

    )J

    00

  • 13; /}O/-I ~J )\ - ?Jr;trj6fj2f/-

    LUe- fill d x C-' C( /) of xy ;'j. C./) , /} TPI/Qrl ~JI 2.. ,

    X J/ -=- (; 1-//)6"t ;e;- '" t- ,) (;027-/)

    ) :J\ /

    c - !.:J I, /0 01 0/ II 0 0 10 0/ oj 01 II

    cvv/d

    /fJ

  • '"--- J""'-4 0- % Cl!Ir. l~f: v ""'-':) v ~':\~ '1--, r;,~

    ~'

    J--- \\

  • 2. (30 Points) For a cyclic code of (8, 5), the generator polynomiaJ is g (p) = 1+ x + x" + x3 .Find all possible codewords. Show how you verify that the generated codewords havecyclic property.

    c\.

    o

    1 (" (1 -; LJ J I / /

    .:1 '-) If U II I )

    (

    (JuDI/liD

    ')/" JoG;

    __ 5 l-I /

    )

    I

    000/0

    ')JIOO

    u/DOl)

    /~/j -I I

    /

    t ) ,'I" 0uOO

    ') J) I 0 ) ') /

    I ) / J l':J/ u

    ') / / ')n/

    Y v -rlI

    (I,J~"-' I

    (

    ') / ()(} (J / rJ()

    /000/0Du o

    ) , 00/01/01

    0/1/.) d/Ol/()/O

    / f / )

    /)' I

    )

    ) /0/

    , "(I ff i P'-::>t/' 107/

    7- S' 'I l/ 1l -1-/) t/Jfl

    ")/ )/')()

    )/0/01"

    '0 /(') I) 1 ()

    O"'}l!/

    0/0/0

    /01 )()

    / ~ l! (J -tt T! f-,?t 6:3.P f ;V , ~ -I ~

    "1/1 dO !lcJ

    I,j/'J)/

  • 3. (30 Points) Answer the following questions as True or False. For the False ones, givethe cOlTect answer or the reason. For the True ones, justify the reason

    ,.--a) lSI originates from transmitting rectangular pulses instead of raised cosine waveforms: ((' 'e-

    ,CC( u)~) j/Yl~'1 r-1f7y'

    riJ('/]

    b) Graded index fibres have less attenuation compared with single mode fibres: ;=v/') ~

    iJ

    c) Channel equalizing is used to cancel the lSI terms:

    )] uf c ~q /} /IU

    01- -i'5) jU-/YlS

    d) Linear codes are obtained by mapping k bits into n bits: Iru L

    a/I

    e) Coding represents a reduction in the dimensionality of the signal space: r~IJ~