Linganisha mbinu

	Nadharia ya Uwezo wa Idhaa ya Shannon	Misimbo ya Polar yenye Uondoaji Mfululizo
Nyanja	Mawasiliano ya Simu	Mawasiliano ya Simu
Familia	Process / pipeline	Process / pipeline
Mwaka wa asili	1948	2009
Mwanzilishi	Claude Shannon	Erdal Arikan
Aina	fundamental theoretical bound	recursive error-correcting code
Chanzo asilia	Shannon, C. E. (1948). A mathematical theory of communication. Bell System Technical Journal, 27(3), 379-423.	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.
Majina mbadala	channel capacity, information theory bound	channel polarization, recursive codes
Zinazohusiana	5	5
Muhtasari	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.	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.