Table of Contents
Why log is used in information theory?
We can call log(1/p) information. Why? Because if all events happen with probability p, it means that there are 1/p events. To tell which event have happened, we need to use log(1/p) bits (each bit doubles the number of events we can tell apart).
How many bits is the information content of a message whose probability is 1 16?
As a quick illustration, the information content associated with an outcome of 4 heads (or any specific outcome) in 4 consecutive tosses of a coin would be 4 bits (probability 1/16), and the information content associated with getting a result other than the one specified would be ~0.09 bits (probability 15/16).
Why is entropy measured in bits?
Information provides a way to quantify the amount of surprise for an event measured in bits. Entropy provides a measure of the average amount of information needed to represent an event drawn from a probability distribution for a random variable.
What is mutual information in information theory?
Mutual information is one of many quantities that measures how much one random variables tells us about another. It is a dimensionless quantity with (generally) units of bits, and can be thought of as the reduction in uncertainty about one random variable given knowledge of another.
Why do we use Shannon entropy?
Shannon’s entropy quantifies the amount of information in a variable, thus providing the foundation for a theory around the notion of information. For example, information may be about the outcome of a coin toss. This information can be stored in a Boolean variable that can take on the values 0 or 1.
Why is the amount of information carried zero?
An alphabet set contains 3 letters A,B, C transmitted with probabilities of 1/3, ¼, 1/4. Find entropy. Ø If there is more uncertainty about the message, information carried is also more. Ø If receiver knows the message being transmitted, the amount of information carried is zero.
How is information content measured?
Numerically, information is measured in bits (short for binary digit; see binary system). One bit is equivalent to the choice between two equally likely choices. When there are several equally likely choices, the number of bits is equal to the logarithm of the number of choices taken to the base two.
Why are bits measured?
Numerically, information is measured in bits (short for binary digit; see binary system). One bit is equivalent to the choice between two equally likely choices. The greater the information in a message, the lower its randomness, or noisiness, and hence the smaller its entropy.
How does mutual information work?
Mutual information is calculated between two variables and measures the reduction in uncertainty for one variable given a known value of the other variable. A quantity called mutual information measures the amount of information one can obtain from one random variable given another.