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CORK INSTITUTE OF TECHNOLOGY
INSTITIÚID TEICNEOLAÍOCHTA CHORCAÍ
Semester 1 Examinations 2008/
Module Title: Communications Engineering
Module Code: ELTR
School: Electrical & Electronic Engineering
Programme Title: Bachelor of Engineering (Honours) in Electronic Engineering - Award
Programme Code: EELXE_8_Y
External Examiner(s): Prof. W. G. Hurley and Dr. S. Foley Internal Examiner(s): Dr. R. A. Guinee
Instructions: Answer any THREE questions.
Duration: 2 Hours
Sitting: Winter 2008
Requirements for this examination:
Note to Candidates: Please check the Programme Title and the Module Title to ensure that you have received the correct examination paper. If in doubt please contact an Invigilator.
Q1 (a) Distinguish between the following code types, ( i ) distinct, ( ii ) uniquely decodable and ( iii ) instantaneously decodable by giving examples for the following source.
Source Alphabet Symbol Probability A 1/ B 1/ C 1/ D 1/ E 1/
Determine the average codeword length and compare this with the source entropy in each of the above cases. (11.5%)
(b) Show that for an n -symbol source X represented by an instantaneously decodable code of length L that H ( X )≤ L where H ( X ) is the source entropy. (11.5%)
(c) A source produces five symbols S 1 , S 2 , S 3 , S 4 and S 5 with probabilities 0.1, 0.25, 0.15, 0.2 and 0.3. Construct an optimal code using the Huffman algorithm for this source. Determine the source entropy and average codeword length. (10.33%)
Q2 (a) Show that for a Linear Block Code the verification procedure used is CH T^ =0 where C is an ( n,k ) block code and H is the parity check matrix. (7%)
(b) The parity check bits of an (8,4) block code are generated by c 5 = d 1 + d 2 + d 4 , c 6 = d 1 + d 2 + d 3 c 7 = d 1 + d 3 + d 4 , c 8 = d 2 + d 3 + d 4 where d 1 , d 2 , d 3 and d 4 are the message bits. Determine (i) the generator and parity check matrices for this code. (ii) determine all codewords associated with this code, its minimum weight and error detection and correction capabilities (12%)
(c) If a (7,4) cyclic code has a generator polynomial g(x)=x 3 +x^2 +1 construct the encoder circuit. Determine the code polynomial for the message d(x)=x 3 +x+1 in systematic form. Is the received code polynomial V(x)=1+x+x^2 +x^4 a valid code and if not determine its syndrome. (14.33%)
P ( e )
E b / No (dB)
Fig.Q4: Error Rates of PSK Modulation Systems
