Information theory is the mathematical study of the quantification, storage, and communication of information. The field was originally established by the works of Harry Nyquist and Ralph Hartley, in the 1920s, and Claude Shannon in the 1940s. The field, in applied mathematics, is at the intersection of probability theory, statistics, computer science, statistical mechanics, information engineering, and electrical engineering.
In telecommunications, orthogonal frequency-division multiplexing (OFDM) is a type of digital transmission used in digital modulation for encoding digital (binary) data on multiple carrier frequencies. OFDM has developed into a popular scheme for wideband digital communication, used in applications such as digital television and audio broadcasting, DSL internet access, wireless networks, power line networks, and 4G/5G mobile communications.
Rate–distortion theory is a major branch of information theory which provides the theoretical foundations for lossy data compression; it addresses the problem of determining the minimal number of bits per symbol, as measured by the rate R, that should be communicated over a channel, so that the source can be approximately reconstructed at the receiver without exceeding an expected distortion D.
Channel capacity, in electrical engineering, computer science, and information theory, is the theoretical maximum rate at which information can be reliably transmitted over a communication channel.
In information theory, the noisy-channel coding theorem, establishes that for any given degree of noise contamination of a communication channel, it is possible to communicate discrete data nearly error-free up to a computable maximum rate through the channel. This result was presented by Claude Shannon in 1948 and was based in part on earlier work and ideas of Harry Nyquist and Ralph Hartley.
In information theory, a relay channel is a probability model of the communication between a sender and a receiver aided by one or more intermediate relay nodes.
In the field of wireless communication, macrodiversity is a kind of space diversity scheme using several receiver or transmitter antennas for transferring the same signal. The distance between the transmitters is much longer than the wavelength, as opposed to microdiversity where the distance is in the order of or shorter than the wavelength.
Multiuser detection deals with demodulation of the mutually interfering digital streams of information that occur in areas such as wireless communications, high-speed data transmission, DSL, satellite communication, digital television, and magnetic recording. It is also being currently investigated for demodulation in low-power inter-chip and intra-chip communication. Multiuser detection encompasses both receiver technologies devoted to joint detection of all the interfering signals or to single-user receivers which are interested in recovering only one user but are robustified against multiuser interference and not just background noise.
Precoding is a generalization of beamforming to support multi-stream transmission in multi-antenna wireless communications. In conventional single-stream beamforming, the same signal is emitted from each of the transmit antennas with appropriate weighting such that the signal power is maximized at the receiver output. When the receiver has multiple antennas, single-stream beamforming cannot simultaneously maximize the signal level at all of the receive antennas. In order to maximize the throughput in multiple receive antenna systems, multi-stream transmission is generally required.
In telecommunications, dirty paper coding (DPC) or Costa precoding is a technique for efficient transmission of digital data through a channel subjected to some interference known to the transmitter. The technique consists of precoding the data in order to cancel the interference. Dirty-paper coding achieves the channel capacity without a power penalty and without requiring the receiver to know the interfering signal.
Multi-user MIMO (MU-MIMO) is a set of multiple-input and multiple-output (MIMO) technologies for multipath wireless communication, in which multiple users or terminals, each radioing over one or more antennas, communicate with one another. In contrast, single-user MIMO (SU-MIMO) involves a single multi-antenna-equipped user or terminal communicating with precisely one other similarly equipped node. Analogous to how OFDMA adds multiple-access capability to OFDM in the cellular-communications realm, MU-MIMO adds multiple-user capability to MIMO in the wireless realm.
Cooperative diversity is a cooperative multiple antenna technique for improving or maximising total network channel capacities for any given set of bandwidths which exploits user diversity by decoding the combined signal of the relayed signal and the direct signal in wireless multihop networks. A conventional single hop system uses direct transmission where a receiver decodes the information only based on the direct signal while regarding the relayed signal as interference, whereas the cooperative diversity considers the other signal as contribution. That is, cooperative diversity decodes the information from the combination of two signals. Hence, it can be seen that cooperative diversity is an antenna diversity that uses distributed antennas belonging to each node in a wireless network. Note that user cooperation is another definition of cooperative diversity. User cooperation considers an additional fact that each user relays the other user's signal while cooperative diversity can be also achieved by multi-hop relay networking systems.
In radio, cooperative multiple-input multiple-output is a technology that can effectively exploit the spatial domain of mobile fading channels to bring significant performance improvements to wireless communication systems. It is also called network MIMO, distributed MIMO, virtual MIMO, and virtual antenna arrays.
In radio, multiple-input and multiple-output (MIMO) is a method for multiplying the capacity of a radio link using multiple transmission and receiving antennas to exploit multipath propagation. MIMO has become an essential element of wireless communication standards including IEEE 802.11n, IEEE 802.11ac, HSPA+ (3G), WiMAX, and Long Term Evolution (LTE). More recently, MIMO has been applied to power-line communication for three-wire installations as part of the ITU G.hn standard and of the HomePlug AV2 specification.
In wireless communication, spatial correlation is the correlation between a signal's spatial direction and the average received signal gain. Theoretically, the performance of wireless communication systems can be improved by having multiple antennas at the transmitter and the receiver. The idea is that if the propagation channels between each pair of transmit and receive antennas are statistically independent and identically distributed, then multiple independent channels with identical characteristics can be created by precoding and be used for either transmitting multiple data streams or increasing the reliability. In practice, the channels between different antennas are often correlated and therefore the potential multi antenna gains may not always be obtainable.
Zero-forcing precoding is a method of spatial signal processing by which a multiple antenna transmitter can null the multiuser interference in a multi-user MIMO wireless communication system. When the channel state information is perfectly known at the transmitter, the zero-forcing precoder is given by the pseudo-inverse of the channel matrix. Zero-forcing has been used in LTE mobile networks.
In linear algebra, the restricted isometry property (RIP) characterizes matrices which are nearly orthonormal, at least when operating on sparse vectors. The concept was introduced by Emmanuel Candès and Terence Tao and is used to prove many theorems in the field of compressed sensing. There are no known large matrices with bounded restricted isometry constants, but many random matrices have been shown to remain bounded. In particular, it has been shown that with exponentially high probability, random Gaussian, Bernoulli, and partial Fourier matrices satisfy the RIP with number of measurements nearly linear in the sparsity level. The current smallest upper bounds for any large rectangular matrices are for those of Gaussian matrices. Web forms to evaluate bounds for the Gaussian ensemble are available at the Edinburgh Compressed Sensing RIC page.
In digital communications, a turbo equalizer is a type of receiver used to receive a message corrupted by a communication channel with intersymbol interference (ISI). It approaches the performance of a maximum a posteriori (MAP) receiver via iterative message passing between a soft-in soft-out (SISO) equalizer and a SISO decoder. It is related to turbo codes in that a turbo equalizer may be considered a type of iterative decoder if the channel is viewed as a non-redundant convolutional code. The turbo equalizer is different from classic a turbo-like code, however, in that the 'channel code' adds no redundancy and therefore can only be used to remove non-gaussian noise.
In mathematics and telecommunications, stochastic geometry models of wireless networks refer to mathematical models based on stochastic geometry that are designed to represent aspects of wireless networks. The related research consists of analyzing these models with the aim of better understanding wireless communication networks in order to predict and control various network performance metrics. The models require using techniques from stochastic geometry and related fields including point processes, spatial statistics, geometric probability, percolation theory, as well as methods from more general mathematical disciplines such as geometry, probability theory, stochastic processes, queueing theory, information theory, and Fourier analysis.
In information theory and telecommunication engineering, the signal-to-interference-plus-noise ratio (SINR) is a quantity used to give theoretical upper bounds on channel capacity in wireless communication systems such as networks. Analogous to the signal-to-noise ratio (SNR) used often in wired communications systems, the SINR is defined as the power of a certain signal of interest divided by the sum of the interference power and the power of some background noise. If the power of noise term is zero, then the SINR reduces to the signal-to-interference ratio (SIR). Conversely, zero interference reduces the SINR to the SNR, which is used less often when developing mathematical models of wireless networks such as cellular networks.
