Vertaile menetelmiä

	LDPC-koodit (Low-Density Parity-Check Codes)	Ortogonaalinen taajuusjakoinen multipleksointi (OFDM)	Polar-koodit peräkkäisellä peruutuskoodinpurulla
Tieteenala	Tietoliikennetekniikka	Tietoliikennetekniikka	Tietoliikennetekniikka
Menetelmäperhe	Process / pipeline	Process / pipeline	Process / pipeline
Syntyvuosi	1962	1971	2009
Kehittäjä	Robert Gallager	Weinstein and Ebert	Erdal Arikan
Tyyppi	linear error-correcting code	multicarrier modulation scheme	recursive error-correcting code
Alkuperäislähde	Gallager, R. G. (1962). Low-density parity-check codes. IRE Transactions on Information Theory, 8(1), 21-28.	Weinstein, S. B., & Ebert, P. M. (1971). Data transmission by frequency-division multiplexing using the discrete Fourier transform. IEEE Transactions on Communication Technology, 19(5), 628-634.	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.
Rinnakkaisnimet	sparse codes, belief propagation codes	multicarrier modulation	channel polarization, recursive codes
Liittyvät	5	5	5
Tiivistelmä	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.	OFDM is a multicarrier modulation technique that divides a wideband channel into many narrowband orthogonal subcarriers. Introduced by Weinstein and Ebert in 1971, it exploits the duality between time and frequency domains to efficiently use spectrum while mitigating intersymbol interference in frequency-selective channels. OFDM is now the standard for high-speed wireless systems including WiFi, cellular LTE, and digital broadcasting.	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.