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EE550_Lecture_02_082708

EE550_Lecture_02_082708 - Lec nr¢Z 5’ $59 Annoumh(D No...

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Unformatted text preview: Lec+nr¢Z-' 5’: $59 Annoumh: (D No class M09549?) C labor 9193) ® Récli'l'iona‘ 1’!on for VS.“ 1- (on DEN) ' ECCQ!’ MC"; on DNAA (GAO an CGL/ («les/ Ckemov 36%" ‘7‘— ¢ 5 an?“ : (“11: Delta, Code, demed AM“, is H». minmum A; S'bmti MM“ amt Mo Jfiflnd‘ .E h ‘3." ' bum 1;] “ twhcmkmbrh“ 1’" 'b b“ L; e 20"} 5+; an”, mg a. (my F; = \ W Ch+~~-+Ln_..g= cad; P E 0 ‘4 CW"'*‘-%= gm MSW? M1 543% Lrs+ .aP WrAsEVMAU kw 5W PM? a; flow ® Rn..- ., W3 each wit-k MM «lawn an?“ cam Aahd’. 0M3 nuM'u! a“ onus {L4} mush! Jew +‘~M day. Lita» Claim? Tkrs cock Um «id-ed all \-b€+ em“. 12949: 14‘ “M143 a s...“ amt mi? Li. M 39“. mum». ,' Am! So, 1' «\- womU Lo. Adam-.1 +14. pal: 014 ct gfiuxli‘m. £N' :3? Column? (Jaw TM: code cm 461161 A" 2:12“ £(f0f51 “‘13 M .u“{ 51 ‘0‘“ 50:“ “WNW _ TM “‘1! [mt awe of; ‘5 DA one. 9:1 94. (3M) (4|ng It Can ma «8‘ 2.44. I. . (‘ em, 2353,:- 7, ._.‘33 Leo-{9 Swap»: 601 are an odd 1 TM»: 5? errors. e' = ‘5 error) on 91mm ' . d ’ CJntMv Emmi Lu: X LI. «3;; radoM Variaue, 1th 2' L2. 923 (es! number Lg,‘£ r>o i Xilvh'c‘ 0/. ' (a. Sh»: ECefx] = [0%) ”5]“- Performance of Chemov bound and Markov bound Consider transmitting an N —bit binary string through a binary symmetric channel with bit—flipping probability (i.e., bit-error probability) 6. Define random variable X to be the number of bit errors in the received binary string. We are interested in the tail distributions of X, i.e., P,{X 2 k} for k = 0, 1, 2, . . . ,N. The exact value of the tail distribution is easy to write but involves a summation that is not easy to understand analytically. Thus, simple upper bounds are often useful. Here we compare the performance of the Chemov and Markov bounds to the exact values of the tail distribution P,‘{X 2 k}: Exact value: P1.{X 2 k} = ilk (1;) 6i(].— 6)N_i, 0 S k g N Markov bound: P,{X 2 k} 3 Mil %, 1 g k g N Performance of Chemov and Markov bound (N=100. 2:001) 10 m Exact value 4, — — — Chemov bound “" Markov bound i Pr (X >= k) (log scale) a, 3 § _. _. °. °. 8 S i _. ol 0 10 20 30 40 50 60 70 80 90 100 ...
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