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01 ·Coding Theory·★ MEMBER·11 min read LDPC and Turbo Codes — The Error Correction Behind 5G and Deep Space Shannon proved in 1948 that these codes exist, and nobody could build one for 45 years. Starting from zero background, this article unpacks the three ideas — soft decisions, log-likelihood ratios, and belief propagation — that finally reached the theoretical limit, and shows what actually runs in 5G NR and deep-space links.