lecture19

# lecture19 - Lecture Outline (Week 11, lecture 1) Channel...

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Lecture Outline (Week 11, lecture 1) Channel Coding – Hamming Code (Continued) Reading: Same as last lecture. 1. Parity Check Codes (Recap) We can represent the codewords as [ ] A I u G u x = = . G is the generator matrix. Parity check codes are known as linear codes, namely the addition of two codewords (bitwise exclusive OR) is also a codeword. Channel corrupts the codeword. We receive e x y + = with errors. Consider each position of y is first hard decoded as 0 or 1. Errors disturb the parity of the selected bits checked. The syndrome, namely the set of disturbed parities, is given more generally by: H y s = . The parity check matrix H is given by = I A H If there is no channel error, G u x y = = , we have zero syndrome since [ ] 0 ) ( = + = = = = A A u I A A I u GH u H y s . Note that the multiplication of the generator matrix G by the parity check matrix H gives a zero matrix. Errors create a nonzero syndrome for the parity bits, unless the error sequence itself

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## This note was uploaded on 11/01/2009 for the course EEE 455 taught by Professor Hui during the Spring '09 term at ASU.

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lecture19 - Lecture Outline (Week 11, lecture 1) Channel...

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