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	Kody LDPC (Low-Density Parity-Check Codes)	Kodowanie polarne z dekodowaniem sukcesywnym anulowaniem	Twierdzenie o pojemności kanału Shannona
Dziedzina	Telekomunikacja	Telekomunikacja	Telekomunikacja
Rodzina	Process / pipeline	Process / pipeline	Process / pipeline
Rok powstania	1962	2009	1948
Twórca	Robert Gallager	Erdal Arikan	Claude Shannon
Typ	linear error-correcting code	recursive error-correcting code	fundamental theoretical bound
Źródło pierwotne	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.	Shannon, C. E. (1948). A mathematical theory of communication. Bell System Technical Journal, 27(3), 379-423.
Inne nazwy	sparse codes, belief propagation codes	channel polarization, recursive codes	channel capacity, information theory bound
Pokrewne	5	5	5
Podsumowanie	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.	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.