homework7e-f_solution_corr

homework7e-f_solution_corr - were correct, and thus we can...

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ECE 5325/6325 Spring 2010: Homework 7(e-f) Solutions 7e: We need to compute r S , where the multiplication is “multiply and then sum mod 2”. (i) r = [1 , 1 , 1 , 1 , 0 , 0 , 0] so r S = [1 , 1 , 1 , 1 , 0 , 0 , 0] 1 1 1 0 1 1 1 0 1 1 1 0 1 0 0 0 1 0 0 0 1 = [3 , 3 , 3] mod 2 = [1 , 1 , 1] Since the product is not [0, 0, 0], there was an error in the received vector. This vector [1, 1, 1] is the frst row is S so the error is in the frst bit. The transmitted bits were thus the frst Four bits but with bit 1 reversed: [0 , 1 , 1 , 1]. (ii) r = [0 , 0 , 0 , 1 , 1 , 1 , 0], so r S = [0 , 0 , 0 , 1 , 1 , 1 , 0] 1 1 1 0 1 1 1 0 1 1 1 0 1 0 0 0 1 0 0 0 1 = [2 , 2 , 0] mod 2 = [0 , 0 , 0] Since the product is all zeros, there was no error. Thus the transmitted bits were the frst Four bits: [0 , 0 , 0 , 1]. (iii) r = [0 , 0 , 1 , 1 , 1 , 1 , 1], so r S = [0 , 0 , 1 , 1 , 1 , 1 , 1] 1 1 1 0 1 1 1 0 1 1 1 0 1 0 0 0 1 0 0 0 1 = [3 , 2 , 2] mod 2 = [1 , 0 , 0] Since the product is not zeros, there was an error. The error code [1 , 0 , 0] is the same as row #5 in S . Thus the received vector should have been [0, 0, 1, 1, 0, 1, 1]. But the frst Four bits
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Unformatted text preview: were correct, and thus we can say that the transmitted bits were thus [0 , , 1 , 1]. ECE 5325/6325 Spring 2010 2 7f: The transmitted coded bit vector is c = d G , with G = 1 1 1 1 1 1 1 1 1 (i) Encoding the data bits d = [1 , 1 , 1], I get that c = [1 , 1 , 1] 1 1 1 1 1 1 1 1 1 = [1 , 1 , 1 , 2 , 2 , 2] mod 2 = [1 , 1 , 1 , , , 0] . (ii) Encoding the data bits d = [0 , , 1], I get that c = [0 , , 1] 1 1 1 1 1 1 1 1 1 = [0 , , 1 , 1 , 1 , 0] mod 2 = [0 , , 1 , 1 , 1 , 0] (iii) Encoding the data bits d = [1 , 1 , 0], I get that c = [1 , 1 , 0] 1 1 1 1 1 1 1 1 1 = [1 , 1 , , 1 , 1 , 2] mod 2 = [1 , 1 , , 1 , 1 , 0]...
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homework7e-f_solution_corr - were correct, and thus we can...

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