# Information Theory - Shannon's Self-Information units

• Mihel
In summary, Information Theory is a branch of mathematics and computer science that studies the quantification, storage, and communication of information. It deals with fundamental limits of data compression, storage, and communication. Claude Shannon, known as the father of Information Theory, introduced the concept of Shannon's Self-Information unit (or bit) to measure the amount of information in a message. This unit is calculated using the logarithm of the inverse probability of an event occurring. Entropy, which measures the average information content in a message, is directly related to Shannon's Self-Information unit. Information Theory has various real-life applications, including data compression, error correction codes, cryptography, and understanding information transmission in living systems.
Mihel
Information Theory - Shannon's "Self-Information" units

Hi,

I'm familiar with information and coding theory, and do know that the units of Shannon information content (-log_2(P(A))) are "bits". Where "bit" is a "binary digit", or a "storage device that has two stable states".

But, can someone rigorously prove that the units are actually "bits"? Or we should only accept it as a definition and then justify it with coding examples.

Thanks!

No, you can use what ever logarithmic base. For natural information you could use unit "nat" with base e and for binary information unit "bit" with base 2.

## 1. What is Information Theory?

Information Theory is a branch of mathematics and computer science that studies the quantification, storage, and communication of information. It deals with the fundamental limits of data compression, data storage, and data communication.

## 2. Who is Shannon and what is Shannon's Self-Information unit?

Claude Shannon was an American mathematician and electrical engineer who is known as the father of Information Theory. Shannon's Self-Information unit, also known as a bit, is the fundamental unit used to measure the amount of information in a message. It represents the amount of uncertainty or randomness in a message.

## 3. How is Shannon's Self-Information unit calculated?

Shannon's Self-Information unit is calculated using the logarithm of the inverse probability of an event occurring. This means that the more unlikely an event is to occur, the higher the amount of information it contains.

## 4. What is the relationship between entropy and Shannon's Self-Information unit?

Entropy is a measure of the average information content in a message. It is directly related to Shannon's Self-Information unit, as the entropy of a message can be calculated by taking the average of the Self-Information units of each symbol in the message.

## 5. How is Information Theory applied in real life?

Information Theory has various applications in everyday life, such as in data compression algorithms used for file compression, in error correction codes used in communication systems, and in cryptography for secure communication. It is also used in fields like biology, neuroscience, and linguistics to study and understand the transmission of information in living systems.

• Introductory Physics Homework Help
Replies
14
Views
1K
• Classical Physics
Replies
18
Views
2K
• Quantum Physics
Replies
24
Views
711
• Thermodynamics
Replies
1
Views
1K
• Programming and Computer Science
Replies
9
Views
3K
• Quantum Interpretations and Foundations
Replies
2
Views
1K
• Quantum Interpretations and Foundations
Replies
25
Views
2K
• Linear and Abstract Algebra
Replies
3
Views
2K
• Quantum Interpretations and Foundations
Replies
7
Views
2K
• Thermodynamics
Replies
1
Views
1K