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| Kody LDPC (Low-Density Parity-Check Codes)× | Twierdzenie o pojemności kanału Shannona× | |
|---|---|---|
| Dziedzina | Telekomunikacja | Telekomunikacja |
| Rodzina | Process / pipeline | Process / pipeline |
| Rok powstania≠ | 1962 | 1948 |
| Twórca≠ | Robert Gallager | Claude Shannon |
| Typ≠ | linear 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. DOI ↗ | Shannon, C. E. (1948). A mathematical theory of communication. Bell System Technical Journal, 27(3), 379-423. DOI ↗ |
| Inne nazwy | sparse codes, belief propagation codes | channel capacity, information theory bound |
| Pokrewne | 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. | 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. |
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