Salīdzināt metodes

	Polārie kodi ar secīgu atcelšanas dekodēšanu	Zemās blīvuma paritātes pārbaudes kodi (LDPC)	Ortogonālā frekvenču multipleksēšana ar sadalītu nesēju (OFDM)	Šenona kanāla ietilpības teorēma
Nozare	Telekomunikācijas	Telekomunikācijas	Telekomunikācijas	Telekomunikācijas
Saime	Process / pipeline	Process / pipeline	Process / pipeline	Process / pipeline
Izcelsmes gads	2009	1962	1971	1948
Autors	Erdal Arikan	Robert Gallager	Weinstein and Ebert	Claude Shannon
Tips	recursive error-correcting code	linear error-correcting code	multicarrier modulation scheme	fundamental theoretical bound
Pirmavots	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.	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.	Shannon, C. E. (1948). A mathematical theory of communication. Bell System Technical Journal, 27(3), 379-423.
Citi nosaukumi	channel polarization, recursive codes	sparse codes, belief propagation codes	multicarrier modulation	channel capacity, information theory bound
Saistītās	5	5	5	5
Kopsavilkums	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.	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.	Shannon's channel capacity theorem, published in 1948, establishes the maximum rate at which information can be reliably transmitted over a noisy channel. Expressed as C = B log2(1 + S/N) for additive white Gaussian noise (AWGN), it is a fundamental bound in information theory and communications engineering. Shannon proved that reliable communication is possible at any rate below capacity, and impossible above it. This theorem underpins the design of all modern communication systems and motivates coding theory, modulation, and signal processing techniques.