# sample - Sample problem 1. 2. 3. 4. 5. Generate the G and H...

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Sample problem 1. Generate the G and H matrix for a Hamming code with r=n-k=3. 2. Determine a code basis 3. Evaluate the minimum distance 4. Evaluate the error correction capability t and the error detection capability e 5. Evaluate the block error probability when the channel transition probability is p=0.002 and p=0.2 (no retransmission) 6. Evaluate the block error probability when the channel transition probability is p=0.002 and p=0.2 (with retransmission) Solution 1. The code parameters will be: n=2 r -1=7, k=n-r=7-3=4. H is built with columns that contain all the combinations of 1, 2, …, r ones (which is 1,2,3 ones). Possible H and G are: = 1 1 1 0 1 0 0 1 0 1 1 0 1 0 1 1 0 1 0 0 1 H = 1 0 0 0 1 1 1 0 1 0 0 1 0 1 0 0 1 0 1 1 0 0 0 0 1 0 1 1 G 2. The rows of G form a possible basis for the code Basis = {(1101000),(0110100),(1010010),(1110001)} 3. Minimum distance d min =3 (it is a property of Hamming codes) 4. 2 1 d e 1 2 1 min min = = = = d

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## This note was uploaded on 04/24/2011 for the course EE 4421 taught by Professor Mondin during the Spring '11 term at California State University Los Angeles .

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sample - Sample problem 1. 2. 3. 4. 5. Generate the G and H...

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