Error Control Coding Asssignment 4 Due 11:00 am Friday 3 June 2011 Value in brackets indicates marks for each question. Total value of marks is 20. This assignment counts towards 12.5% of the total assessment. Question 1 (6): A (15,11) cyclic code has the generator polynomial g ( X ) = 1+ X + X 4 . (a) Show that this code does not have any code words of weight 1 or 2. (b) Show that there are at least 30 code words of weight 3. (Hint: use g ( X ) and g ( X ) 2 .) (c) Devise a systematic encoder for this code. (d) Devise a Meggitt decoder for this code. Question 2 (4): We have the generator polynomial g ( X ) + 1 ) X 2 ) X 4 ) X 6 ) X 7 ) X 10 (a) Show that g ( X ) generates a (21,11) cycle code. (b) Devise a syndrome computation circuit for this code. (b) Let r ( X ) + 1 ) X 5 ) X 17 be a received polynomial. Compute the syndrome of r ( X ). Display the contents of the syndrome register after each digit of r has been shifted into the syndrome com-putation circuit. Question 3 (4): Let
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Coding theory, Error detection and correction, syndrome computation circuit