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Unformatted text preview: Mimic Theorem 8.6.5 in the text. See also Chapter 12. 9. A Second Chance I Suppose that W is a random variable with alphabet W . Let ˆ W 1 and ˆ W 2 denote two guesses of W . Let P e denote the probability that both guesses are wrong P e = Pr( W 6 = ˆ W 1 and W 6 = ˆ W 2 ) . Since there is no point in repeating a guess, we assume that ˆ W 1 6 = ˆ W 2 with probability 1. (a) Show that H ( P e ) + P e log( |W| -2) + (1-P e ) ≥ H ( W | ˆ W 1 , ˆ W 2 ) . (b) Under what conditions does this inequality hold with equality? 10. A Second Chance II Consider a channel coding scenario in which the decoder gets two chances to correctly guess the transmitted message. We say that an error has occurred if both guesses are incorrect. Let C 2 denote the capacity of the channel under this setup, and let C denote the usual Shannon capacity. (a) Explain why C 2 ≥ C . (b) Does C 2 = C ? Prove or disprove....
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This note was uploaded on 10/03/2011 for the course ECE 5620 at Cornell.