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hw3 - Boston University Department of Electrical and...

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Boston University Department of Electrical and Computer Engineering ENG EC515 Digital Communication ( Fall 2009 ) Problem set 3 Assigned: Mon 5 Oct Due: Mon 12 Oct Suggested reading: Class-notes, handouts, and Ch. 4 textbook O ffi ce hours: M, W 4:00–5:30pm PHO438 Problem 3.1 (Optimum receiver) A communication system is used to transmit one of two equally likely messages, M ∈ M = { 1 , 2 } . The channel output is a voltage (a continuous random variable), Y R , whose conditional density function is given by: p Y | M ( y | 1) = y 0 y 1 2 - y 1 y 2 0 otherwise p Y | M ( y | 2) = ( 0 . 25 - 1 y 3 0 otherwise (a) Determine b m opt ( y ) the optimum (minimum probability of error) receiver decision rule. (b) Compute P e the resulting probability of error. Problem 3.2 ( Value of noisy look at noise) A communication system is used to transmit one of two equally likely messages, M ∈ M = { 1 , 2 } . The channel inputs are voltage levels (real numbers). The channel encoder uses a real channel codebook con-
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