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In channel coding, you often generate and modulate the codeword all at zero to test performance of a decoder.

(For example codeword = zeros (1,n); x = 2*codeword-1)

in other cases the codeword is generated and modulate from :word = rand(1,n); codeword = mod(word*G,2);x = 2*codeword-1).

n: length of codeword; G: Generator matrix.

What is the difference between its two ways of proceeding and what is the advantage of generating and modeling a code word all at zero?

m2016b
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    If the code is [linear](https://en.wikipedia.org/wiki/Linear_code) (as is often the case), any codeword has the same behaviour in terms of error performance. The all-zero codeword is just simpler to use. For example, the distance from any other word C to the all-zero word is just the [Hamming weight](https://en.wikipedia.org/wiki/Hamming_weight) of C – Luis Mendo Jun 27 '17 at 09:49
  • Thanks @Luis Mendo. I understand now. So, if I do simulations with its two options, I have to have the same curves? – m2016b Jun 27 '17 at 10:27
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    If the code is linear yes, you will get the same error curves, up to statistical fluctuations – Luis Mendo Jun 27 '17 at 10:28
  • I have done the tests on my decoder (ordering statistics decoding) and I find a good error curve with the all-zero codeword, but with the second option I find an error curve almost contante.My decoder must have a problem? I use the Golay code (24,12,8). – m2016b Jun 27 '17 at 11:36
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    No idea with the information you provide, sorry – Luis Mendo Jun 27 '17 at 11:52
  • No problem,thank you for your explanation which allowed me to understand the advantage of generating the all-zero code word. – m2016b Jun 27 '17 at 12:10

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