Stanford EE274: Data Compression - Beyond IID Distributions: Conditional Entropy - Lecture 8
Explore conditional entropy and advanced data compression techniques beyond IID distributions in this Stanford lecture, enhancing understanding of complex information theory concepts.
Asymmetric Numeral Systems (ANS) - Data Compression Lecture 7
Explore Asymmetric Numeral Systems (ANS), an advanced data compression technique, in this Stanford lecture. Gain insights into its principles, applications, and advantages in modern compression algorithms.
Coding Theory
This course provides an introduction to traditional and modern coding theory. Topics covered include linear block codes, cyclic codes (BCH and RS codes), convolutional codes, turbo codes and low-density parity-check (LDPC) codes.
The Thermodynamics of Communication - Exploring Energy and Information Limits
Exploring the fundamental relationship between energy, information, and matter in communication processes. Discusses nonlinear dynamics of communication channels and their implications for collective intelligence and limits to human knowledge.
Advanced Linear Algebra
Comprehensive exploration of advanced linear algebra concepts, including least squares approximation, error-correcting codes, functional calculus, affine transformations, and stochastic maps, with practical applications.
An Introduction to Lifted Expander Graphs - Fernando Granha Jeronimo
Explore lifted expander graphs, their construction, and applications in theoretical computer science. Learn about symmetry structures, coding theory implications, and recent advancements in this field.
Locally Testable Codes with Constant Rate, Distance, and Locality, Part I - Irit Dinur
Explore locally testable codes with constant rate, distance, and locality. Learn about a new construction based on left-right Cayley complexes, addressing an open question in coding theory.
High Dimensional Expansion and Error Correcting Codes - Irit Dinur
Explore high-dimensional expansion, error-correcting codes, and their connections. Delve into expansion constructions, property testing, and revolution complexes with expert Irit Dinur.
Pseudorandom Error-Correcting Codes with Applications to Watermarking Generative AI
Explore the innovative framework of pseudorandom error-correcting codes and their application in watermarking AI-generated content, focusing on cryptographic implementations and robustness guarantees.
Algebraic Attacks for the Rank Decoding Problem - Lecture 2
Explorez les attaques algébriques pour le problème du décodage de rang dans cette conférence mathématique approfondie, axée sur les avancées récentes et les techniques avancées.
Algebraic Attacks for the Rank Decoding Problem - Lecture 1
Explorez les attaques algébriques pour le problème du décodage de rang dans cette conférence mathématique approfondie, mettant l'accent sur les concepts clés et les techniques avancées.
DNAe2c Error Correction Code for DNA Data Storage - 10x Improvement Over Reed Solomon Codes
Discover advanced error correction techniques for DNA data storage through DNAe2c, achieving 10x better performance than Reed Solomon codes with minimal overhead for improved data integrity and storage efficiency.
Cover Your Bases: Minimizing Sequencing Coverage in DNA Storage Systems
Explores minimizing DNA sequencing coverage in storage systems, focusing on error-correcting codes and retrieval algorithms to reduce costs and latency while optimizing information retrieval efficiency.
Great Ideas in Theoretical Computer Science - Polynomials
Explore theoretical computer science through polynomials, covering fields, division, evaluation, interpolation, and error-correcting codes. Gain insights into fundamental concepts and their applications.
Locally Testable Codes with Constant Rate, Distance, and Locality
Explore breakthroughs in locally testable codes, focusing on constant rate, distance, and locality. Irit Dinur discusses high-dimensional expanders, Tanner codes, and local testability proofs.
Building Manifolds from Error Correcting Codes - IPAM at UCLA
Explore the intersection of error correcting codes and manifold construction, delving into quantum error correction, topology, and complex mathematical concepts.
High Dimensional Expanders - Introduction and Motivation
Explore high-dimensional expanders, their applications in error-correcting codes, and the motivations behind this emerging field of mathematics and computer science.
Periods, Shafarevich Maps and Applications - Nodal Surfaces and Coding Theory
Explore nodal surfaces and coding theory in K3 geometry. Learn about period maps, Torelli theorem, and binary codes in relation to polarized nodal K3 surfaces and their components.
Monomial Ideals Arising from Graph Theory and Coding Theory
Explore connections between monomial ideals, graph theory, and coding theory in this advanced mathematics talk by Keri Sather-Wagstaff from Clemson University.
Codes from Polynomials Over Finite Fields
Explore polynomial-based coding theory, focusing on Reed-Solomon and Reed-Muller codes, their properties, and applications in error correction for reliable data transmission over noisy channels.
Small-Set Expansion in the 2-Degree Short-Code Graph - The Easier Version
Explore the intricacies of small-set expansion in the 2-degree short-code graph, focusing on an easier version of this complex mathematical concept.