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Unformatted text preview: EC EY ECEF ED EA ED EAA E School of Computer and Communication Sciences Principles of Digital Communications: Assignment date: April 26, 2007 Summer Semester 2009 Due date: April 26, 2007 Solution Midterm Exam Problem 1. (Bhattacharyya Bound and Laplacian Noise) (a) It is an upper bound to the probability that a MAP decoder makes an error given that H = 0. Equality holds if the decoder chooses H = 1 whenever there is a tie. (b) It is an upper bound to the probability that a MAP decoder makes the correct decision given that H = 1. Equality holds if the decoder always chooses H = 1 when there is a tie. (c) integraldisplay j radicalBig f Y | H ( y | 0) f Y | H ( y | 0) = integraldisplay y f Y | H ( y | 0) = 1 (1) (d) f Y | H ( y | 0) = 1 2 e-| y + a | f Y | H ( y | 1) = 1 2 e-| y- a | We need to compute B ( a ) = integraldisplay - radicalbigg 1 4 e-| y + a | e-| y- a | dy = I + II + III where I = integraldisplay- a- 1 2 e ( y + a )+( y- a ) dy = 1 2 integraldisplay a- e y...
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