Linganisha mbinu

	Kuweka Nambari kwa Njia ya Turbo na Uondoaji wa Nambari kwa Njia ya Iterative	Misimbo ya Usahihishaji Makosa ya Msongamano Mdogo (LDPC)
Nyanja	Mawasiliano ya Simu	Mawasiliano ya Simu
Familia	Process / pipeline	Process / pipeline
Mwaka wa asili	1993	1962
Mwanzilishi	Claude Berrou, Alain Glavieux, and Punya Thitimajshima	Robert Gallager
Aina	iterative error-correcting code	linear error-correcting code
Chanzo asilia	Berrou, C., Glavieux, A., & Thitimajshima, P. (1993). Near Shannon limit error-correcting coding and decoding: Turbo-codes. In Proceedings of the IEEE International Conference on Communications (ICC), 1064-1070.	Gallager, R. G. (1962). Low-density parity-check codes. IRE Transactions on Information Theory, 8(1), 21-28.
Majina mbadala	iterative decoding, concatenated codes	sparse codes, belief propagation codes
Zinazohusiana	5	5
Muhtasari	Turbo codes, introduced by Berrou, Glavieux, and Thitimajshima in 1993, are a landmark in channel coding history. They achieve performance within 0.5 dB of the Shannon limit—the theoretical boundary for reliable communication—a feat previously thought impossible with practical complexity. Turbo codes use concatenated convolutional codes with an interleaver and iterative decoding via belief propagation. They were adopted in 3G (UMTS) and remain important in 4G/5G systems alongside 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.