final_exam

# final_exam - EE 5501 Digital Communication Prof Jindal Dec...

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EE 5501 Prof. Jindal Digital Communication Dec. 19, 2009 Final Exam The exam has 4 questions, for a total of 100 points. For all problems except the first, you must show your work to receive credit. 1. Nyquist Criterion (10 pts) For each of the following waveforms, indicate whether it satisfies the Nyquist criterion, and whether it is a square-root Nyquist pulse. The symbol period is T = 2. For each part circle your answers. You do not need to show your work for this question. (a) Nyquist: Yes No Square-root Nyquist: Yes No (5 pts) (b) Nyquist: Yes No Square-root Nyquist: Yes No (5 pts)

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2. Constellations (20 pts) In each of the following parts, you are given two constellations (the constellation points are indicated by X’s). Determine which of the two constellations has a larger d min , assuming that the constellations are scaled to have the same energy per-bit . (a) (4 pts) Constellation 1 Constellation 2 (b) (4 pts) Constellation 1 Constellation 2
(c) (4 pts) Constellation 1 Constellation 2

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(d) (8 pts) Constellation 1 Constellation 2
3. Punctured Convolutional Codes (35 pts) High-rate convolutional codes can be derived from lower rate convolutional codes through the process of puncturing . Puncturing refers to deleting some of the coded bits output by the encoder. By deleting (i.e., puncturing) some of the bits, the total number of coded bits is decreased and therefore the rate of the code is increased. (The pattern with which bits are deleted, i.e., the puncturing pattern, is fixed and is known to both the encoder and decoder.)

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