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ex2_makeup

# ex2_makeup - ECE320 Makeup Second Examination Cornell...

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ECE320 Makeup Second Examination Spring 2006 Cornell University T.L.Fine CLOSED BOOK, NO NOTES, CALCULATORS, OR SCRAP PAPER. TURN OFF CELLPHONES. ALLOTTED TIME IS 1 hour and 30 min. SHOW YOUR WORK, GIVE REASONS, NOT JUST ANSWERS. Place your three-digit ID number, not your name, on each sheet. Work each problem on a separate sheet of paper so that the individual questions can be separated for grading. 1. Consider a source with five symbols [a,b,c,d,e] having correspond- ing probabilities of being chosen of p = [1 , 1 , 2 , 4 , 8] / 16. Consider a prefix code for this set of symbols with the corresponding codewords being [0000 , 0001 , 001 , 01 , 1]. (a)(2pts) What is the expected codeword length? (b)(3pts) Calculate the source entropy H in bits. (c)(4pts) Construct a Huffman code for this source, evaluate its expected length, and compare it to the entropy found in (b). (d)(6pts) Consider the set of codewords [00 , 01 , 10 , 11 , 1] for the symbols listed in (a). Evaluate the expected codeword length and compare it to the expected length found in (c). Comment on the comparison.

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