Cours6 - Chap 4 Elements of Information Theory ELEC 2880...

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Chap 4: Elements of Information Theory ELEC 2880: Modem Design () Chap 4: Elements of Information Theory ELEC 2880: Modem Design 1 / 11
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Elements of Information Theory Introduction Given a channel/environment What is the best information rate that can be transmitted? For a given performance/reliability = Capacity of the channel What parameters have influence? Information Theory Define ”information” contained in a message as mathematical quantity Depends on probability of the message Define ”mutual information” Information obtained by observing message passed through channel (with noise) Consider values averaged on all possible realizations Mathematical proof of best that can be done (see other course) () Chap 4: Elements of Information Theory ELEC 2880: Modem Design 2 / 11
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Information Basic Idea More information is obtained by unlikely events - There are clouds in the sky - There is a rainbow - There is a big meteorite falling down Information depends of probability of event (or message) I ( p ) Function is decreasing with p Information of independent events add up I ( p 1 p 2 ) = I ( p 1 ) + I ( p 2 ) Def: Information of an event or message x k I ( x k ) = - log 2 p ( x k ) All log in base 2!! (proportionality coefficient) Unit of information is bit Ex: A bit with 2 equiprobable values p ( x k ) = 0 . 5 gives 1 bit of information Ex:
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