22-Elec-B3 Digital Communications Systems, December 2014: worked solutions

Paper format: Professional Engineers of Ontario, Annual Examinations — December 2014, 07-Elec-B3 Digital Communication Systems. Three hours, closed book, a PEO-approved non-programmable calculator permitted. Five questions are printed at 25 marks each; any four constitute a complete paper worth 100 marks, and only the first four appearing in the answer book are marked. Marks are shown in the left margin. All five questions are solved below, because the set as a whole is the study resource.

Reference texts.

S. Haykin, Communication Systems, 5th ed. — the primary reference for link budgets, digital modulation, matched-filter detection and error-control coding.
B. P. Lathi and Z. Ding, Modern Digital and Analog Communication Systems, 4th ed. — source coding, Huffman codes, Nyquist signalling and channel capacity.
J. G. Proakis and D. G. Manolakis, Digital Signal Processing: Principles, Algorithms and Applications, 4th ed. — convolution and discrete-time filtering background for Question 4.

Check — the parity-check matrix of Question 5(c) did not print on the paper. Page 3 reads “Consider a binary Hamming code with the following parity check matrix:” followed by a blank gap of roughly two lines, and then “Give the corresponding generator matrix.” The gap is genuinely empty: the matrix is missing from the printed paper itself. Parts (c) and (d) are therefore solved for the standard systematic binary (7,4) Hamming code, which is the only binary Hamming code that fits a matrix of the size the gap allows and is the canonical textbook example. The assumption is stated explicitly in the answer, exactly as Note 1 on the cover page instructs (“the candidate is urged to submit with the answer paper a clear statement of any assumptions made”). The method of parts (c) and (d) is independent of which particular Hamming matrix is intended.

22-Elec-B3 Digital Communications Systems: December 2014