Information Theory, Coding and Cryptography

Information Theory, Coding and Cryptography. Instructor: Dr. Ranjan Bose, Department of Electrical Engineering, IIT Delhi. Information theory, coding and cryptography are the three load?bearing pillars of any digital communication system. In this introductory course, we will start with the basics of information theory and source coding. Subsequently, we will discuss the theory of linear block codes (including cyclic codes, BCH codes, RS codes and LDPC codes), convolutional codes, Turbo codes, TCM and space time codes. Finally, we will introduce the basics of secure communications by focusing on cryptography and physical layer security. Wherever possible, applications of the theory in real world scenarios have been provided. The underlying aim of this course is to arouse the curiosity of the students. (from

Lecture 27 - Generator Polynomial Matrix, Syndrome Polynomial Matrix, Catastrophic and ...

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Source Coding
Lecture 01 - Introduction to Information Theory
Lecture 02 - Average Mutual Information, Entropy, Conditional Entropy, Joint Entropy
Lecture 03 - Information Measures for Continuous Random Variables, Relative Entropy
Lecture 04 - Variable Length Codes, Kraft Inequality, Source Coding Theorem
Lecture 05 - Source Coding Theorem, Efficiency of a Code, Huffman Coding, Coding in Blocks
Lecture 06 - Huffman Coding, Arithmetic Coding, Lempel Ziv Coding, Run Length Coding
Lecture 07 - Optimal Quantizer, Entropy Rate, Some Practical Applications of Source Coding
Lecture 08 - Introduction to Superinformation
Channel Capacity and Coding
Lecture 09 - Channel Models, Channel Capacity, Symmetric Channels, Noisy Channel Coding Theorem
Lecture 10 - Symmetric Channels, Noisy Channel Coding Theorem, Repetition Code, Gaussian Channel
Lecture 11 - Gaussian Channel, Information Capacity Theorem, Shannon Limit
Lecture 12 - Information Capacity Theorem, Shannon Limit, Capacity of MIMO Channels
Linear Block Codes
Lecture 13 - Introduction to Error Control Coding, Block Codes, Hamming Distance and Weight
Lecture 14 - Block Codes, Hamming Distance, Hamming Weight, and Examples
Lecture 15 - Linear Block Codes, Equivalent Codes, Generator Matrix, Parity Check Matrix
Lecture 16 - Systematic Code, Singleton Bound, Maximum Distance Code, Error Detection and Correction
Lecture 17 - Erasures and Errors, Cosets, Standard Array, Syndrome Decoding
Lecture 18 - Probability of Error, Coding Gain, Hamming Bound, Perfect Code
Lecture 19 - Hamming Codes, LDPC Codes, Optimal Codes, MDS Codes
Cyclic Codes
Lecture 20 - Introduction to Cyclic Codes
Lecture 21 - Cyclic Codes: Generator Polynomial, Syndrome Polynomial, Matrix Representation
Lecture 22 - Fire Code, Golay Codes, CRC Codes, Circuit Implementation, Meggitt Decoder
Bose-Chaudhuri Hocquenghem (BCH) Codes
Lecture 23 - Introduction to BCH Codes: Generator Polynomials
Lecture 24 - Multiple Error Correcting BCH Codes, Decoding of BCH Codes
Reed Solomon Codes
Lecture 25 - Introduction to Reed Solomon Codes
Convolutional Codes
Lecture 26 - Introduction to Convolutional Codes
Lecture 27 - Generator Polynomial Matrix, Syndrome Polynomial Matrix, Catastrophic and Non Catastrophic Codes, Free Distance, Modified State Diagram
Lecture 28 - Matrix Description, Viterbi Decoding Algorithm, Bounds
Turbo Codes
Lecture 29 - Introduction to Turbo Codes
Trellis Coded Modulation (TCM)
Lecture 30 - Introduction to Trellis Coded Modulation
Lecture 31 - Ungerboeck's Design Rules, Performance Evaluation of TCM Schemes
Lecture 32 - TCM for Fading Channels, Space Time Trellis Codes, Rayleigh Fading Scenario
Space Time Codes
Lecture 33 - Introduction to Space Time Block Codes (STBC)
Lecture 34 - Real Orthogonal Design, Complex Orthogonal Design
Lecture 35 - Real Orthogonal Design, Complex Orthogonal Design (cont.)
Lecture 36 - Introduction to Cryptography: Symmetric Key and Asymmetric Key Cryptography
Lecture 37 - Some Well-Known Algorithms: DES, IDEA, PGP, DH Protocol
Lecture 38 - Introduction to Physical Layer Security: Notion of Secrecy Capacity
Lecture 39 - Secrecy Outage Capacity, Secrecy Outage Probability, Cooperative Jamming