Exercise-3.sol - THE UNIVERSITY OF WESTERN ONTARIO FACULTY...

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FACULTY OF ENGINEERING ECE-433b-COMMUNICATION SYSTEMS Exercise-3 (Solutions) 1) Consider the CRC-16 code described by the generator polynomial 1 2 15 16 + + + X X X . Using examples demonstrate the various error detection properties of the code. Please work out this yourself. Refer to course notes on CRC. 2) Consider the (5, 1) repetition code. Evaluate the syndrome s for the following error patterns: a. All five possible single-error patterns; b. All 10 possible double-error patterns. The generator polynomial for ) 1 , 5 ( code is: [ ] k I P G = = [ ] 1 1111 . Therefore, [ ] T k n P I H - = = 1 1 0 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 0 1 and = 1 1 1 1 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 T H , S=e T H , where e is the error pattern. Single Error Patterns Syndrome 0 0 0 0 1 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 1 0 0 0 0 1 0 0 1 0 0 0 0 1 0 0 1 0 0 0 0 1 0 0 0 Two Error Patterns Syndrome 0 0 0 11 1 1 1 0
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Exercise-3.sol - THE UNIVERSITY OF WESTERN ONTARIO FACULTY...

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