手法を比較

	逐次消去復号による極座標符号	低密度パリティ検査符号（LDPC）	Multiple-Input Multiple-Output (MIMO)	シャノンチャネル容量定理
分野	通信工学	通信工学	通信工学	通信工学
系統	Process / pipeline	Process / pipeline	Process / pipeline	Process / pipeline
提唱年	2009	1962	1995	1948
提唱者	Erdal Arikan	Robert Gallager	Telatar, Foschini, and Gans	Claude Shannon
種類	recursive error-correcting code	linear error-correcting code	spatial multiplexing technique	fundamental theoretical bound
原典	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.	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.	Shannon, C. E. (1948). A mathematical theory of communication. Bell System Technical Journal, 27(3), 379-423.
別名	channel polarization, recursive codes	sparse codes, belief propagation codes	spatial multiplexing, antenna diversity	channel capacity, information theory bound
関連	5	5	5	5
概要	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.	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.	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.