practice_final

practice_final - EE 5501 Digital Communication Prof. N....

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EE 5501 Prof. N. Jindal Digital Communication Dec. 16, 2009 Practice Problems for Final Exam 1. Consider the following three waveforms: s 0 ( t ) = ( 1 0 t 1 0 else s 1 ( t ) = ( - 1 Δ 0 t Δ 0 else s 2 ( t ) = ( - 1 1 - Δ Δ t 1 0 else Assume equal message priors, i.e., π (0) = π (1) = π (2), white Gaussian noise with variance σ 2 = N 0 / 2, and that Δ is a constant between 0 and 1. (a) Find an orthonormal basis for the waveforms and provide the signal space repre- sentation in terms of this basis. (b) Sketch the ML decision regions for this constellation. (c) Is P e | 1 increasing or decreasing in Δ? (d) Derive the union bound for this constellation. 2. Consider the R = 1 / 3 binary convolutional code with memory 2 that outputs the following three coded bits for each information bit: u [ k ] + u [ k - 1] + u [ k - 2] u [ k ] + u [ k - 1] + u [ k - 2] u [ k ] + u [ k - 2] (in octal notation this is the [7,7,5] code) (a) Draw the trellis diagram (with outputs labeled for each branch) for this code.
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This note was uploaded on 11/21/2011 for the course EE 5501 taught by Professor Lops during the Fall '08 term at Minnesota.

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practice_final - EE 5501 Digital Communication Prof. N....

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