1. The transpose of the H matrix for a systematic linear block code is H' = XXXXXXXXXX...

Question

1. The transpose of the H matrix for a systematic linear block code is H' = XXXXXXXXXX XXXXXXXXXX1111M, OMNI'  •  a) Write down a table containing all the codewords for this code, and their hamming weights.  b) Suppose the information block is x„., = [101]. What is the signal space vector, sm , corresponding to the signal that gets transmitted? Assume the energy per coded bit is E.  c) Write down an upper bound for the probability of error, given that the sm from part (b) is transmitted, i.e. an upper bound for P(elsm), assuming soft decision decoding is used.
	
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Robert · Accepted Answer

Assignment -1500 
Question 1 
Part a) 
First calculate G , code generator then  
Cm= XmG 
H=[P| I] 
G=[I| transpose(P)]
H is already in standard form so  
P is given by first three rows 
And hence  
1 0 0 1 1 0
0 1 0 0 1 1
0 0 1 1 1 0
G
 
 

 
  
xm Cm  = XmG Wm 
= number of 
ones in Cm 
0 0 0 000000 0 
0 0 1 001110 3 
0 1 0   010011 3 
0 1 1 011101 4 
1 0 0 100110 3 
1 0 1 101000 2 
1 1 0 110101 4 
1 1 1 111011 5
Part b) 
Xm =[101] 
And from above table cm =[10100] 
Energy is Ec 



N
n
nmncm tfCEts
1
)()12()(    
Hence  
Sm =  [sqrt(Ec) ,- sqrt(Ec),

1. The transpose of the H matrix for a systematic linear block code is H' = XXXXXXXXXX XXXXXXXXXX1111M, OMNI' • a) Write down a table containing all the codewords for this code, and their hamming...

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