LDPC Codes
LDPC codes, invented by Robert Gallager in 1962 and rediscovered in the 1990s by MacKay, are linear error-correcting codes defined by sparse parity-check matrices. They achieve performance within 0.4 dB of the Shannon limit with iterative belief-propagation decoding and have become the standard for modern wireless (WiFi-6, 5G NR, Digital Video Broadcasting). Unlike turbo codes, LDPC codes have a more elegant graph-theoretic structure and more mature theoretical analysis.
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- Gallager, R. G. (1962). Low-density parity-check codes. IRE Transactions on Information Theory, 8(1), 21-28. · DOI 10.1109/TIT.1962.1057683
- Richardson, T. J., & Urbanke, R. L. (2001). The capacity of low-density parity-check codes under message-passing decoding. IEEE Transactions on Information Theory, 47(2), 599-618. · DOI 10.1109/18.910577
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