InfoCoBuild

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 nptel.ac.in)

Lecture 30 - Introduction to Trellis Coded Modulation

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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

Superinformation

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.)

Cryptography

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