# Mutual And Self Information Entropy Pdf

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## Digital Communication - Information Theory

Information is the source of a communication system, whether it is analog or digital. Information theory is a mathematical approach to the study of coding of information along with the quantification, storage, and communication of information. These three events occur at different times. The difference in these conditions help us gain knowledge on the probabilities of the occurrence of events. When we observe the possibilities of the occurrence of an event, how surprising or uncertain it would be, it means that we are trying to have an idea on the average content of the information from the source of the event.

Entropy can be defined as a measure of the average information content per source symbol. Where p i is the probability of the occurrence of character number i from a given stream of characters and b is the base of the algorithm used.

The amount of uncertainty remaining about the channel input after observing the channel output, is called as Conditional Entropy. Now, considering both the uncertainty conditions before and after applying the inputs , we come to know that the difference, i.

Mutual information of a channel is related to the joint entropy of the channel input and the channel output. We have so far discussed mutual information. The maximum average mutual information, in an instant of a signaling interval, when transmitted by a discrete memoryless channel, the probabilities of the rate of maximum reliable transmission of data, can be understood as the channel capacity.

A source from which the data is being emitted at successive intervals, which is independent of previous values, can be termed as discrete memoryless source. This source is discrete as it is not considered for a continuous time interval, but at discrete time intervals.

This source is memoryless as it is fresh at each instant of time, without considering the previous values. Digital Communication - Information Theory Advertisements. Previous Page. Next Page. Previous Page Print Page. Dashboard Logout.

## Digital Communication - Information Theory

Cross Validated is a question and answer site for people interested in statistics, machine learning, data analysis, data mining, and data visualization. It only takes a minute to sign up. I'm not a statistic major, so my knowledge of statistics is quite limited but I've found myself in need of learning about and using mutual information. I believe I understand the concept and formula, but it seems counter-intuitive that perfectly similar data would have 0 mutual information. I would expect two sets of data with perfect similarity to have mutual information of 1. I'm writing a program which calculates Mutual Information between two columns i and j in a pairwise protein sequence, and I'm not sure if I should manually fix the MI to be 1 if the columns are exactly the same. For example, if the two columns written as lines were:.

In probability theory and information theory , the mutual information MI of two random variables is a measure of the mutual dependence between the two variables. More specifically, it quantifies the "amount of information" in units such as shannons , commonly called bits obtained about one random variable through observing the other random variable. The concept of mutual information is intimately linked to that of entropy of a random variable, a fundamental notion in information theory that quantifies the expected " amount of information " held in a random variable. MI is the expected value of the pointwise mutual information PMI. The quantity was defined and analyzed by Claude Shannon in his landmark paper A Mathematical Theory of Communication , although he did not call it "mutual information".

This document is an introduction to entropy and mutual information for discrete random variables. It gives their definitions in terms of prob- abilities, and a few.

## Mutual information

The universe is overflowing with information. Everything must follow the rules of information theory, no matter the format. With information theory, we can measure and compare how much information is present in different signals. In this section, we will investigate the fundamental concepts of information theory and applications of information theory in machine learning.

Imagine that someone hands you a sealed envelope, containing, say, a telegram. You want to know what the message is, but you can't just open it up and read it. Instead you have to play a game with the messenger: you get to ask yes-or-no questions about the contents of the envelope, to which he'll respond truthfully.

Information theory is a subfield of mathematics concerned with transmitting data across a noisy channel. A cornerstone of information theory is the idea of quantifying how much information there is in a message. More generally, this can be used to quantify the information in an event and a random variable, called entropy, and is calculated using probability. Calculating information and entropy is a useful tool in machine learning and is used as the basis for techniques such as feature selection, building decision trees, and, more generally, fitting classification models.

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#### Mutual Information

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3 Response
1. Bob F.

Information is the source of a communication system, whether it is analog or digital.

2. Forrest B.

Which horse won? Dr. Yao Xie, ECE, Information Theory, Duke University. 2. Page 4.

3. Fabienne A.

Updated 07 Mar