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# hw4 - EE 5501 Digital Communication Homework 4 Due Tuesday...

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EE 5501 Prof. N. Jindal Digital Communication Oct. 7, 2009 Homework 4 Due: Tuesday, Oct. 13, 12:30 PM 1. 3.15 You do not need to solve part (c), but can use its result for the rest of the problem. 2. 3.13 (a) and (b) For part (b), find the intelligent union bound for an inner point and for an outer point, and combine these to get the intelligent union bound on the probability of error. 3. 3.17 (a) and (b) 4. Consider anitpodal binary signaling, where message 0 corresponds to the point - A and message 1 corresponds to the point A . The message probabilities are π (0) and π (1). (a) The optimal decision rule is of the form δ ( y ) = ( 0 y T 1 y > T for the optimal threshold T . Derive an expression for T in terms of A , σ 2 and π (0). (b) Is T increasing or decreasing in π (0)? Explain. (c) Assume π (0) = 0 . 75. What happens to the threshold T and the probability of error as the noise variance goes to infinity (i.e., σ 2 → ∞ )? (d) Show that the probability of error with π (0) = 0 . 75 is less than or equal to the probability of error when π (0) = 0 . 5.

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• Fall '09
• xyz
• error probability, signal space representation, Prof. N. Jindal, intelligent union bound, equal message probabilities

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