'Systematic code' diaporamas de présentation

Error control coding for wireless communication technologies. Background material for Hamming codes. EU-USA Atlantis Programme. FIT & Budapest University of Technology and Economics. Objective. Design a code which can correct every single error . Motivation :

Error control coding for wireless communication technologies. Background material for linear error control codes Janos Levendovszky. EU-USA Atlantis Programme. FIT & Budapest University of Technology and Economics. Challenge.

296.3:Algorithms in the Real World. Error Correcting Codes I Overview Hamming Codes Linear Codes. message (m). coder. codeword (c). noisy channel. codeword’ (c’). decoder. message or error. General Model. Errors introduced by the noisy channel:

296.3:Algorithms in the Real World. Error Correcting Codes II Cyclic Codes Reed-Solomon Codes. Viewing Messages as Polynomials. A (n, k, n-k+1) code: Consider the polynomial of degree k-1 p(x) = a k-1 x k-1 + L + a 1 x + a 0 Message : (a k-1 , …, a 1 , a 0 )

Results

Cyclic Code. Linear Block Code. Hamming Code is a Linear Block Code. Linear Block Code means that the codeword is generated by multiplying the message vector with the generator matrix.