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

• Notes
• 11

This preview shows pages 1–4. Sign up to view the full content.

Chap 4: Elements of Information Theory ELEC 2880: Modem Design () Chap 4: Elements of Information Theory ELEC 2880: Modem Design 1 / 11

This preview has intentionally blurred sections. Sign up to view the full version.

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
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:

This preview has intentionally blurred sections. Sign up to view the full version.

This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern