#Coding-Theory
4 posts in tag “Coding-Theory”.
Error-Correcting Codes: Reed-Solomon, LDPC, and How Distributed Storage Survives Failure
2025-05-18Build error-correcting codes from the ground up: finite field arithmetic, Reed-Solomon encoding and decoding via Lagrange interpolation, LDPC codes and belief propagation, and how modern distributed storage systems use erasure coding to survive disk failures with minimal overhead.
Shannon's Information Theory from First Principles: Entropy, Channel Capacity, and the Fundamental Limits of Communication
2025-03-05Build Shannon's information theory from the ground up: entropy as a measure of uncertainty, source coding theorem, channel capacity, and the noisy-channel coding theorem that established the theoretical limits of reliable communication.
Combinatorial Designs and Coding Theory: Block Designs, Steiner Systems, and Finite Geometry
2022-10-10An exploration of combinatorial design theory—block designs, Steiner systems, finite projective planes—and their deep connections to error-correcting codes and experimental design.
Algebraic Geometry in Computer Science: Gröbner Bases, the Nullstellensatz, and Applications in Cryptography and Coding Theory
2022-08-21A rigorous exploration of how algebraic geometry—Gröbner bases, Hilbert's Nullstellensatz, and elliptic curves—powers modern cryptography, error-correcting codes, and complexity theory.