Linganisha mbinu

	Misimbo ya Usahihishaji Makosa ya Msongamano Mdogo (LDPC)	Misimbo ya Polar yenye Uondoaji Mfululizo
Nyanja	Mawasiliano ya Simu	Mawasiliano ya Simu
Familia	Process / pipeline	Process / pipeline
Mwaka wa asili	1962	2009
Mwanzilishi	Robert Gallager	Erdal Arikan
Aina	linear error-correcting code	recursive error-correcting code
Chanzo asilia	Gallager, R. G. (1962). Low-density parity-check codes. IRE Transactions on Information Theory, 8(1), 21-28.	Arikan, E. (2009). Channel polarization: A method for constructing capacity-achieving codes for symmetric binary-input memoryless channels. IEEE Transactions on Information Theory, 55(7), 3051-3073.
Majina mbadala	sparse codes, belief propagation codes	channel polarization, recursive codes
Zinazohusiana	5	5
Muhtasari	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.	Polar codes, introduced by Erdal Arikan in 2009, are the first constructive family of codes proven to achieve the Shannon capacity of symmetric binary-input memoryless channels. They use recursive construction and successive cancellation decoding, a simple greedy algorithm with theoretical guarantees. Polar codes were adopted in 5G NR for control channel coding and are studied for future 6G systems. Unlike turbo and LDPC codes (which are empirical), polar codes provide rigorous theoretical foundations.