# Exercise-2 - (c Compute the syndrome for the received...

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THE UNIVERSITY OF WESTERN ONTARIO FACULTY OF ENGINEERING ECE-433b-COMMUNICATION SYSTEMS Exercise-2 [Release Date: January 23, 2007] 1. Show that the final parity check in a horizontal and vertical parity check code, if taken as the modulo 2 sum of all the data bits, is equal to the modulo 2 sum of the horizontal parity checks and is also equal to the modulo 2 sum of the vertical parity checks. 2. Find an example of a pattern of six errors that cannot be detected by the use of horizontal and vertical parity checks. 3. Consider a (7,4) code whose generator matrix is G= 1 0 0 0 0 1 1 0 0 0 0 1 1 0 0 0 1 0 1 0 1 0 0 0 1 1 1 1 (a) Find the Coefficient matrix, P; Find all the code words of the code; (b) Find parity check matrix H for the code.
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Unformatted text preview: (c) Compute the syndrome for the received vector r=[1101101] (d) Is the received vector a valid code word? (e) What is the error correcting capability of the code? (f) What is the error-detecting capability of the code? 4. Consider a systematic block code whose parity-check equations are: 3 2 1 3 2 1 2 3 2 1 3 1 m m m b m m m b m m m b m m m b + + = + + = + + = + + = Where i m are message bits and i b are parity check bits. (a) Find the Generator matrix G and the parity check matrix H for this code. (b) How many errors can the code correct? (c) How many errors can the code detect? (d) Is the vector [10101010] Try these problems yourself; no need to submit solutions...
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• Spring '08
• Choi
• Coding theory, Hamming Code, University of Western Ontario, parity check, Vertical Parity Checks, 1 1 1 1 0 0 0 1 0 1 0 1 0 0 G

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