Vertaile menetelmiä

	LDPC-koodit (Low-Density Parity-Check Codes)	Monitulo-monitulo (MIMO)	Polar-koodit peräkkäisellä peruutuskoodinpurulla
Tieteenala	Tietoliikennetekniikka	Tietoliikennetekniikka	Tietoliikennetekniikka
Menetelmäperhe	Process / pipeline	Process / pipeline	Process / pipeline
Syntyvuosi	1962	1995	2009
Kehittäjä	Robert Gallager	Telatar, Foschini, and Gans	Erdal Arikan
Tyyppi	linear error-correcting code	spatial multiplexing technique	recursive error-correcting code
Alkuperäislähde	Gallager, R. G. (1962). Low-density parity-check codes. IRE Transactions on Information Theory, 8(1), 21-28.	Telatar, I. (1999). Capacity of multi-antenna Gaussian channels. European Transactions on Telecommunications, 10(6), 585-595.	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	spatial multiplexing, antenna diversity	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.	MIMO is a technique that uses multiple transmit and receive antennas to significantly increase channel capacity and reliability. Pioneered theoretically by Telatar (1999) and Foschini & Gans (1998), MIMO exploits multipath propagation—typically a liability in wireless—as an asset by creating independent spatial channels. It is now fundamental to all modern wireless systems including LTE, WiFi-6, and 5G, where it provides both capacity gains through spatial multiplexing and robustness through diversity.	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.