Error detection and error correction — from parity bits to Reed-Solomon, turbo codes, and beyond. A comprehensive journey through the mathematics that keeps our digital world reliable.
Shannon's theorem, noisy channels, Hamming distance, and the fundamental limits of reliable communication
Parity bits, repetition codes, ISBN check digits, and the building blocks of error detection
Richard Hamming's elegant single-error-correcting codes, SECDED, and perfect codes
Cyclic redundancy checks, polynomial arithmetic over GF(2), and the workhorses of error detection
Generator matrices, syndrome decoding, dual codes, and the mathematical framework for block codes
Shift-register encoders, trellis diagrams, and the Viterbi algorithm that powered deep space exploration
Multi-error-correcting codes, minimal polynomials, and the bridge to Reed-Solomon
The world's most deployed error-correction code — from CDs to deep space to QR codes
The 1993 breakthrough that came within a whisker of Shannon's limit and revolutionised communications
Gallager's rediscovered codes, Tanner graphs, belief propagation, and the codes inside Wi-Fi and 5G
LT codes, Raptor codes, and the elegant idea of generating unlimited encoded symbols
Arikan's provably capacity-achieving codes, channel polarisation, and the 5G control channel standard
Deep space, QR codes, Blu-ray, 5G, RAID, submarine cables — where coding theory meets the real world