Prob3Sol - l“) I |.. M v (M- U -'I- lCC‘l‘i if)?“...

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Unformatted text preview: l“) I |.. M v (M- U -'I- lCC‘l‘i if)?“ Dalia-1 CONN]lli]ll(1éll’.l()]lH Iii-rill 20] 'l Pinhlmn Sm: 3 Him in class. [l-fl’mvdagg. Owl. 121,11. 1301]. i liiltl iislu'il you Lu (hi this iii class: Find the. (lii'l'{-:J'(éiill.iail entropy (il' a mm 11105131 r-rmiplm: Gaussian i'amdmn \ieii'ii-ihlt-é with \-’éi]'l£1.ll('10()l'rffl. 1,15ingilhs. iiml the iimtual iiil’oriiiziiimi ('Jl' El ('Uiiiplox AWGN cilinmiol, l" a»: X --l« N. whvm X m (INTO. 51) am] A" (7,»‘\i"((}. This is ilw capacity ol‘ {hit (:(iiiiplux s\\-\-"(1'.il {'hmnwl " ' . Show that llw (lil'lbi'mit.in.l viiii'cipy of a long;th Gaussian l'eiiiilmn \ioclzm‘ X. m NH]. 0‘; Zl MK) :1: 3 lt.)g._3(27r(i)”§C§. \\'lif‘i'(‘ [Ci (101101105 the (l(!ii{,‘i'!11ll]fl.ilt ol" the ('(.)\-‘£1.]'i‘(1.l'l('i(“. llll-llli'ix C. ‘ . POI-133: (‘hniizit‘l has 1% possith inputsT X 2 a. b ()1’ r: and {.wu possilalv onipiils i” l m' '2. \3\-'(.\ know that Pl)" :7; B/X ; a) U and FOR I: l/X I: h) :2:- Pwr : MN 7;: r) \::.:. ]/-3_ \'\7heii is tho Uplzii'iial input iliHh'ihilLimi and llllt‘ overall {annuity of this (:lizuiiwl? Him: inputs b and (r ham: the ammo tmnsition iiifobeil)ililzim. 136.60: Slightly (lilll‘n'aiit from when. i had said l would pill; (in the l'l\\-‘" in class: In £1. hhiiii'y (317131111! (".l'iniiiml hits “(.lira;i.;i]_)(‘21.i"’ without. ])I'(.)l'):l.l)llli.l\v‘ }) (output Hileitc ii"). (\lsv hilzh‘ em: i‘ci‘xéivml wilhuni. (:‘ifi'Ul', Lu, PO” :::: l./X :4: l .2: l. i p ;.:,.. PU" ()fX :4: 0) MN] 1’0"" (r/X s: (l) PU” :4 (i/X :«22 l.) :-=-:: j). ll" .l"(.=\.' 2:: (l) _::: n:, ilrrl'c‘i'iiiiiit.‘ [the Hml‘llnl iiilk'ii'nmliun [(X; as n l’mictimi ()i’ a, Then the mhiu of n- Lhm I]H]Xlil]l%(‘h‘ HA7; l") mu] llOiHK“ the channel captivity. ECE— 520 him/if 3 Q Ii WMqu 1 fm AUO*‘J::£LH%£¥m@r, Y|x (V Cal/Ugo”) ram/'ch Mw- MW) ll bjfleC¢l+Ex) ’ L :— (SjfiEca-d Z r Tr$NK 5&2} J w WV“ ’°( Viz) ».-.— ”; 1’04: 5M4: “IV—*9) HCY)= Hg<-%U-1’J) HMI“) '—- l’ “WM-=09 + (“-WWYlyk-Ewc) W—fi—m b)” @flqu 2 z 3:; /&,_';C,,7,fl~z 1:; L111,\Ek),v 5 [H’ \M’ ‘r V t " r. V c .3. 3 '73? ‘ . [\F, \ [’1 Y”): KU—I’J 17(Yulro—«Aum (7K Yea) r P 1(1/‘erHW1J4CWm 2' —°<(‘-‘P) C‘jffl‘m _ pygmy) (saga/('4) + (m9) (oath?) “ U252 umwij’) —oy4':«-v 03*? 5 HEM) _( [4”) £24 KM ’g A 5 '/1 ...
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Prob3Sol - l“) I |.. M v (M- U -'I- lCC‘l‘i if)?“...

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