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Information Theory & Coding Book
Contents:
1. Probability and Random Process
Introduction, Basic Terminologies Reltaed to Probability, Mathematical or Classical or ‘A Priori’ Probability, Statistical Defination of Probability, Axiomatic Defination of Probability, Algebra of Events, Properties of Probability, Conditional Probability, Theorem of Total Probability and Baye’s Theorem, Random Variables, Statistical Averages, Probability Distributions, Random Process, Method of Description of a Random Process, Markov Process, Stationary Process, Mean and Autocorrelation of a Random Process.
2. Measures of Information
Introduction, Information Content of a Message, Axioms for the Amount of Information (Self Information), Entropy, Joint and Conditional Uncertainities (Entropies), Relationships Among Different Entropies (Uncertainties), A Measure of Mutual Information.
3. Channels and Their Classification
Discrete Memoryless Channels, Representation of Channel, Classification of Discrete Channels, Channel Capacity, Continuous Channels, Variability of the Continuous Entropy with Coordinate System, Mutual Information I(X, Y), Maximization of the Entropy of a Continuous Random Variable, Shannon-Hartley Theorem, Capacity of a Channel of Infinite Bandwidth.
4. Measures of Information
Introduction, Necessary and Sufficient Conditions for the Existence of Instantaneous Codes, Necessary and Sufficient Condition for Existence of Uniquely, DecIpherable Codes, The Noiseless Coding Theorem, Optimal Code, Shannon’s Binary Code, Huffman Encoding, Higher Extension Code.
5. Error Control Coding (Linear Block Codes)
Introduction, Types of Errors, Decoding Schemes, Relation between Hamming Distance and Error Correcting Capability of Codes, Parity Check Codes, Block Codes, Linear Block Codes, Parity Check Equation and Matrix, Relation between Parity Check Matrix and Generator Matrix, Concept of Group, Decoding Scheme, Decoding-Syndrome and its properties, Decoding-Linear Block Codes, Construction of Single Error Correcting Codes.
6. Error Control Coding (Cyclic Codes-1)
Introduction, Rings and Fields, Ideal, Quotient Rings (Rings of Residue Classes) and Polynomial Rings, Relation of Divisibility in Integers and Polynomials, Galois Fields, Cyclic Codes, Systematic and Non Systematic Cyclic Codes, Matrix description of Cyclic Codes, Decoding oif Cyclic Codes.
7. Error Control Codes (Cyclic Codes-2)
Introduction, Linear Switching Circuits, Encoding using A (n – k) Bit-Shift Register, Decoding using (n – k) Bit Shift Register, Meggitt Decoders for Cyclic Codes, Burst Error Detecting and Correcting Codes, Interlaced Codes for Burst and Random Error Correction, Concatenated codes, Bose-Chaudhari-Hocquengham (BCH) Codes.
8. Error Control Coding (Convolutional Codes)
Discrete Memoryless Channels, Encoding-Convolutional Codes, Code Tree State Diagram and Trellis Diagram, Decoding of Convolutional Codes, Free Distance of a Convolutional Code, Performance of Convolutional Codes, Performance of Block Codes-Error Correction, Performance of Block Codes-Error Detection.
1. Probability and Random Process
Introduction, Basic Terminologies Reltaed to Probability, Mathematical or Classical or ‘A Priori’ Probability, Statistical Defination of Probability, Axiomatic Defination of Probability, Algebra of Events, Properties of Probability, Conditional Probability, Theorem of Total Probability and Baye’s Theorem, Random Variables, Statistical Averages, Probability Distributions, Random Process, Method of Description of a Random Process, Markov Process, Stationary Process, Mean and Autocorrelation of a Random Process.
2. Measures of Information
Introduction, Information Content of a Message, Axioms for the Amount of Information (Self Information), Entropy, Joint and Conditional Uncertainities (Entropies), Relationships Among Different Entropies (Uncertainties), A Measure of Mutual Information.
3. Channels and Their Classification
Discrete Memoryless Channels, Representation of Channel, Classification of Discrete Channels, Channel Capacity, Continuous Channels, Variability of the Continuous Entropy with Coordinate System, Mutual Information I(X, Y), Maximization of the Entropy of a Continuous Random Variable, Shannon-Hartley Theorem, Capacity of a Channel of Infinite Bandwidth.
4. Measures of Information
Introduction, Necessary and Sufficient Conditions for the Existence of Instantaneous Codes, Necessary and Sufficient Condition for Existence of Uniquely, DecIpherable Codes, The Noiseless Coding Theorem, Optimal Code, Shannon’s Binary Code, Huffman Encoding, Higher Extension Code.
5. Error Control Coding (Linear Block Codes)
Introduction, Types of Errors, Decoding Schemes, Relation between Hamming Distance and Error Correcting Capability of Codes, Parity Check Codes, Block Codes, Linear Block Codes, Parity Check Equation and Matrix, Relation between Parity Check Matrix and Generator Matrix, Concept of Group, Decoding Scheme, Decoding-Syndrome and its properties, Decoding-Linear Block Codes, Construction of Single Error Correcting Codes.
6. Error Control Coding (Cyclic Codes-1)
Introduction, Rings and Fields, Ideal, Quotient Rings (Rings of Residue Classes) and Polynomial Rings, Relation of Divisibility in Integers and Polynomials, Galois Fields, Cyclic Codes, Systematic and Non Systematic Cyclic Codes, Matrix description of Cyclic Codes, Decoding oif Cyclic Codes.
7. Error Control Codes (Cyclic Codes-2)
Introduction, Linear Switching Circuits, Encoding using A (n – k) Bit-Shift Register, Decoding using (n – k) Bit Shift Register, Meggitt Decoders for Cyclic Codes, Burst Error Detecting and Correcting Codes, Interlaced Codes for Burst and Random Error Correction, Concatenated codes, Bose-Chaudhari-Hocquengham (BCH) Codes.
8. Error Control Coding (Convolutional Codes)
Discrete Memoryless Channels, Encoding-Convolutional Codes, Code Tree State Diagram and Trellis Diagram, Decoding of Convolutional Codes, Free Distance of a Convolutional Code, Performance of Convolutional Codes, Performance of Block Codes-Error Correction, Performance of Block Codes-Error Detection.
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