tut4_sol - EE 4212 Information and Coding Solution to...

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1 EE 4212 Information and Coding Solution to Tutorial 4 1. A ( n , k ) Linear Block Code = 1 0 0 0 1 1 1 0 1 0 0 0 1 1 0 0 1 0 1 0 1 0 0 0 1 1 1 0 G (a) n = 7 and k = 4. As the dimension of G is 4 x 7, this is a (7,4) Hamming code. (b) There are a total of 2 4 = 16 valid code vectors. m U = mG m U = mG 0000 0 0 0 0 0 0 0 1000 0 1 1 1 0 0 0 0001 1 1 1 0 0 0 1 1001 1 0 0 1 0 0 1 0010 1 1 0 0 0 1 0 1010 1 0 1 1 0 1 0 0011 0 0 1 0 0 1 1 1011 0 1 0 1 0 1 1 0100 1 01 0 1 0 0 1100 1 1 0 1 1 0 0 0101 0 1 0 0 1 0 1 1101 0 0 1 1 1 0 1 0110 0 1 1 0 1 1 0 1110 0 0 0 1 1 1 0 0111 1 0 0 0 1 1 1 1111 1 1 1 1 1 1 1 (c) = = 1 1 1 0 1 1 1 0 1 1 1 0 1 0 0 0 1 0 0 0 1 1 0 1 1 1 0 0 1 1 0 1 0 1 0 1 1 1 0 0 0 1 T H H
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2 (d) The code can identify 2 n-k = 8 error patterns, including the all-zero pattern. Error Pattern
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  • Spring '11
  • wadewe
  • Coding theory, Hamming Code, Error detection and correction, block error probability, 0000000 1110001 1100010 0010011 1 01 0 1 0 0 0100101 0110110 1000111 m

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tut4_sol - EE 4212 Information and Coding Solution to...

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