ps2_ee550_fall08

ps2_ee550_fall08 - UNIVERSITY OF SOUTHERN CALIFORNIA, FALL...

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Unformatted text preview: UNIVERSITY OF SOUTHERN CALIFORNIA, FALL 2008 1 EE 550: Problem Set # 2 Due: Monday Sept. 15, 2008 I. MARKOV AND CHEBYSHEV INEQUALITY Let X be a random variable with mean E { X } and variance σ 2 (i.e., V ar ( X ) = σ 2 ). Use the Markov inequality to prove the Chebyshev inequality Pr {| X- E { X }| ≥ kσ } ≤ 1 k 2 . (Hint: Define Y = ( X- E { X } ) 2 .) II. BIT STUFFING Book problem 2.31. III. FLAGS Book problem 2.35. IV. HAMMING DISTANCE Design a code with at least 3 codewords that has d min = 3 , and that contains a 5-bit undetectable error. V. CRC AND CODE POLYNOMIALS Consider a code with generator G ( D ) = D 4 + D + 1 (so that L = 4 ). Suppose we have a data sequence 0011011 , so that K = 7 and S ( D ) = D 4 + D 3 + D + 1 . a) Consider a convolution code with X ( D ) = S ( D ) G ( D ) . Compute X ( D ) , and give the corresponding 11-bit binary sequence that is transmitted. Does the string 0011011 appear anywhere in this 11-bit sequence? (Note: Recall that for mod- 2 arithmetic, we have 1 + 1 = 0 (or, equivalently, 1 =- 1 ), so that D j + D j = 0 .) b) Suppose we have an error sequence 01010000000 , so that E ( D ) = D 9 + D 7 , and the received polynomial is Y ( D ) = X ( D ) + E ( D ) . Note that this represents an error burst of duration 3 . Use polynomial division to show that this error is....
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This note was uploaded on 12/21/2010 for the course EE 550 taught by Professor Neely during the Fall '08 term at USC.

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ps2_ee550_fall08 - UNIVERSITY OF SOUTHERN CALIFORNIA, FALL...

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