方法对比

	低密度奇偶校验码 (LDPC)	多输入多输出 (MIMO)	极化码（Polar Codes）及其串行消除译码	香农信道容量定理
领域	电信	电信	电信	电信
方法族	Process / pipeline	Process / pipeline	Process / pipeline	Process / pipeline
起源年份	1962	1995	2009	1948
提出者	Robert Gallager	Telatar, Foschini, and Gans	Erdal Arikan	Claude Shannon
类型	linear error-correcting code	spatial multiplexing technique	recursive error-correcting code	fundamental theoretical bound
开创性文献	Gallager, R. G. (1962). Low-density parity-check codes. IRE Transactions on Information Theory, 8(1), 21-28.	Telatar, I. (1999). Capacity of multi-antenna Gaussian channels. European Transactions on Telecommunications, 10(6), 585-595.	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.
别名	sparse codes, belief propagation codes	spatial multiplexing, antenna diversity	channel polarization, recursive codes	channel capacity, information theory bound
相关	5	5	5	5
摘要	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.	MIMO is a technique that uses multiple transmit and receive antennas to significantly increase channel capacity and reliability. Pioneered theoretically by Telatar (1999) and Foschini & Gans (1998), MIMO exploits multipath propagation—typically a liability in wireless—as an asset by creating independent spatial channels. It is now fundamental to all modern wireless systems including LTE, WiFi-6, and 5G, where it provides both capacity gains through spatial multiplexing and robustness through diversity.	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.