Linganisha mbinu

	Misimbo ya Usahihishaji Makosa ya Msongamano Mdogo (LDPC)	Uhamilishaji wa Mgawanyo wa Marudio wa Orthogonal (OFDM)	Nadharia ya Uwezo wa Idhaa ya Shannon
Nyanja	Mawasiliano ya Simu	Mawasiliano ya Simu	Mawasiliano ya Simu
Familia	Process / pipeline	Process / pipeline	Process / pipeline
Mwaka wa asili	1962	1971	1948
Mwanzilishi	Robert Gallager	Weinstein and Ebert	Claude Shannon
Aina	linear error-correcting code	multicarrier modulation scheme	fundamental theoretical bound
Chanzo asilia	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.
Majina mbadala	sparse codes, belief propagation codes	multicarrier modulation	channel capacity, information theory bound
Zinazohusiana	5	5	5
Muhtasari	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.