{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

practice_final

practice_final - EE 5501 Digital Communication Prof N...

This preview shows pages 1–2. Sign up to view the full content.

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. (b) Compute d free for this code.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.
• Fall '08
• LOPS
• Error detection and correction, Convolutional code, Turbo code, White Gaussian noise, binary convolutional code, BCJR algorithm

{[ snackBarMessage ]}

Page1 / 2

practice_final - EE 5501 Digital Communication Prof N...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online