Claude shannon father of the information age youtube. The expectation value of a real valued function f x is given by the integral on x. The capacity c of the channel is the maximum rate for. For a continuous random variable x with pdf fx, define the differential entropy of x as. Therefore, it makes sense to con ne the information carriers to discrete sequences of symbols, unless di erently stated. Chapter1 introduction information theory is the science of operations on data such as compression, storage, and communication. Merchant, department of electrical engineering, iit bombay. Y where the maximum is taken over all possible input distribution p x.
The highest rate in bits per channel use at which information can be sent. Examples of novel topics for an information theory text include asymptotic mean stationary sources, onesided sources as well as twosided sources, nonergodic sources, d continuous channels. This chapter introduces some of the basic concepts of information theory, as well as the definitions. The channel is said to be memoryless if the probability distribution of the output depends only on the input at that time and is conditionally independent of previous channel inputs or outputs. Information theory authorstitles recent submissions 25. Shannons sampling theory tells us that if the channel is bandlimited, in place of the signal we can consider its samples without any loss. We define the information channel capacity of a discrete. Harvard seas es250 information theory now consider an arbitrary discrete memoryless channel x,py x,y followed by a binary erasure channel, resulting in an output y. A discrete time information source x can then be mathemati cally modeled by a. Capacity of a discrete channel as the maximum of its mutual information over.
Mod01 lec01 introduction to information theory and. In this introductory chapter, we will look at a few representative examples which try to give a. Information theory communications and signal processing. As long as source entropy is less than channel capacity, asymptotically errorfree. We shall often use the shorthand pdf for the probability density function px x. Several of the generalizations have not previously been treated in book form. Given a continuous pdf fx, we divide the range of x into bins of width. Introduction to information theory and coding channel coding data. A basic idea in information theory is that information can be treated very much. An ensemble is just a random variable x, whose entropy was defined in eqt 4. Considered the founding father of the electronic communication age, claude shannons work ushered in the digital revolution. Appendix b information theory from first principles stanford university. What is the joint entropy hx, y, and what would it be if the random variables x.
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