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## Introduction to Information Theory and Coding Notes

Data is the wellspring of a correspondence framework, regardless of whether it is simple or computerized. Data hypothesis is a numerical way to deal with the investigation of coding of data alongside the evaluation, stockpiling, and correspondence of data.

States of Occurrence of Events

• On the off chance that we think about a function, there are three states of event.
• On the off chance that the function has not happened, there is a state of vulnerability.
• On the off chance that the function has quite recently happened, there is a state of shock.
• On the off chance that the function has happened, a period back, there is a state of having some data.

Consequently, these three happen at various occasions. The distinction in these conditions assists us with having information on the probabilities of event of functions.

1. Entropy

At the point when we watch the conceivable outcomes of event of a function, regardless of whether shock or dubious it would be, it implies that we are attempting to have a thought on the normal substance of the data from the wellspring of the function.

Entropy can be characterized as a proportion of the normal data content per source image. Claude Shannon, the “father of the Information Theory”, has given an equation for it as

$$H = – \sum_{i} p_i\log_{b}p_i$$

Where $p_i$ is the likelihood of the event of character number I from a given stream of characters and b is the base of the calculation utilized. Thus, this is additionally called as Shannon’s Entropy.

The measure of vulnerability staying about the channel contribution subsequent to watching the channel yield is called as Conditional Entropy. It is signified by $H(x \arrowvert y)$

2. Discrete Memory less Source

A source from which the information is being radiated at progressive stretches, which is free of past qualities, can be named as discrete memory less source.

This source is discrete as it isn’t considered for a constant time stretch, yet at discrete time spans. This source is memory less as it is new at every moment of time, without thinking about the past qualities.

Source Coding

As per the definition, “Given a discrete memory less wellspring of entropy $H(\delta)$, the normal code-word length $\bar{L}$ for any source encoding is limited as $\bar{L}\geq H(\delta)$”.

In less difficult words, the code-word (For instance: Morse code for the word QUEUE is – .- ..- . ..- . ) is consistently more prominent than or equivalent to the source code (QUEUE in model). Which implies, the images in the code word are more noteworthy than or equivalent to the letters in order in the source code.

3. Channel Coding

The divert coding in a correspondence framework, presents repetition with a control, to improve the unwavering quality of the framework. Source coding decreases excess to improve the effectiveness of the framework.

• Channel coding comprises of two parts of activity.
• Planning approaching information grouping into a channel input arrangement.
• Back tracking the channel yield arrangement into a yield information succession.
• The last objective is that the general impact of the channel commotion ought to be limited.
• The planning is finished by the transmitter, with the assistance of an encoder, while the converse planning is done at the beneficiary by a decoder

### Information Theory and Coding Notes and Study Material PDF Free Download

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Here, is a list of a few important notes for a thorough preparation of the Information Theory and Coding course program-

• Information Theory and Coding Notes PDF
• Information Theory and Coding Handwritten Notes PDFs
• Information Theory and Coding Notes for CSE PDFs
• Information Theory and Coding Question Paper PDFs
• Information Theory and Coding PPT Notes PDF

### Information Theory and Coding Reference Books

Books are a rich source of information and students should refer to books that provide excellent conceptual background. Candidates can avail the best books for Information Theory and Coding as recommended by the experts of the subject.

Pupils can refer and read through the Information Theory and Coding Books and other Study Sources during your preparation.

The list of best and highly recommended books for  Information Theory and Coding preparation are as follows, and candidates can choose the book that meets their knowledge and prepare accordingly.

• “Information Theory and Coding” by N Abramson
• “Information Theory” by R B Ash
• “Error Control Coding” by Shu Lin and D J Costello
• “Information Theory and Coding Basics and Practices” by Veluswamy S
• “Information Theory and Coding” by Muralidhar Kulkarni and K S Shivaprakasha
• “Two-Dimensional Information Theory and Coding – With Applications to Graphics Data and High-Density Storage Media” by Jorn Justesen and Soren Forchhammer
• “Fundamentals in Information Theory and Coding” by Borda
• “Information Theory, Coding and Cryptography” by BOSE
• “Information Theory and Coding by Example” by Mark Kelbert Michael Kelbert Yuri Suhov
• “Fundamentals of Information Theory and Coding Design” by Jacob J S Sullum and Christopher J S Desilva

### Information Theory and Coding Curriculum

The best way to make your preparation effective is with an initial idea and an outline of the Information Theory and Coding Syllabus. Keeping in mind every student’s requirements, we have provided a detailed view of the Information Theory and Coding curriculum.

Information Theory and Coding Course Curriculum will give students a clear idea of what to study, and the unit-wise break up gives topics under each unit carefully and allot time to each topic.

Students must cover all the topics before attempting the Information Theory and Coding exam so that the paper is reasonably comfortable at the time of the exam. Candidates must ensure awareness of the Information Theory and Coding Syllabus as it prevents you from wasting unnecessary time on redundant topics.

The updated unit-wise breakup of the Information Theory and Coding Syllabus is as follows-

 Unit Topics UNIT I: Information Theory Uncertainty, Information, Entropy Discrete Memoryless Channel Mutual Information Channel Capacity Shannon’s Theorems Gaussian Channel Limits to Communication UNIT II-Linear Block Codes Groups, Fields and Vector Spaces Construction of Galois Fields of Prime Order Syndrome Error Detection Standard Array and Syndrome Decoding Hamming Codes UNIT III- Cyclic Codes Polynomial Representation of Codewords Generator Polynomial Systematic Codes Generator Matrix Syndrome Calculation and Error Detection Decoding of Cyclic Codes UNIT IV- Structure and Properties of Convolutional Codes Convolutional Encoder Representation Tree, Trellis, and State Diagrams Distance Properties of Convolutional Codes Punctured Convolutional Codes and Rate Compatible Schemes UNIT V- Decoding of Convolutional Codes Maximum Likelihood Detection The Viterbi Algorithm UNIT VI- Automatic Repeat Request Strategies Basic Techniques Hybrid ARQ UNIT VII- Introduction to Cryptography History. Overview of cryptography Simple classical cryptosystems Cryptanalysis UNIT VIII- Perfect Secrecy Information theoretic security One time pad UNIT IX- Secret and Public Key Encryption Description of DES Description of AES (advanced encryption standard) Trapdoor Function The RSA Algorithm

### List of Information Theory and Coding Important Questions

Candidates studying Information Theory and Coding can go through the list of essential questions mentioned below for the Information Theory and Coding course programme. All the given review questions aim to help the candidates to excel in the examination.

• What is entropy?
• What is channel redundancy?
• Name the two source coding techniques.
• Write the expression for code efficiency in terms of entropy.
• What is a memoryless source? Give an example.
• Explain the significance of the entropy H(X/Y) of a communication system where X is the transmitter and Y is the receiver.
• What is information theory?
• Explain Shannon-Fano coding.
• Define bandwidth efficiency.
• Define the channel capacity of the discrete memoryless channel.

### Frequently Asked Questions on Information Theory and Coding Notes

Question 1.
What is the prefix code?

In prefix code, no codeword is the prefix of any other codeword. It is variable length code. The binary digits (codewords) are assigned to the messages as per their probabilities of occurrence.

Question 2.
Define the information rate.

Information rate(R) is represented in average number of bits of information per second. It is calculated as,

R = r H Information bits / sec

Question 3.
Calculate the entropy of the source with a symbol set containing 64 symbols each with a probability pi = 1/ 64 .

Here, there are M = 64 equally likely symbols. Hence entropy of such source is given as,H = log 2 M = log 2 64 = 6 bits / symbol

Question 4.
State the channel coding theorem for a discrete memoryless channel.