Error correction codeIn computing, telecommunication, information theory, and coding theory, forward error correction (FEC) or channel coding is a technique used for controlling errors in data transmission over unreliable or noisy communication channels. The central idea is that the sender encodes the message in a redundant way, most often by using an error correction code or error correcting code (ECC). The redundancy allows the receiver not only to detect errors that may occur anywhere in the message, but often to correct a limited number of errors.
Coding theoryCoding theory is the study of the properties of codes and their respective fitness for specific applications. Codes are used for data compression, cryptography, error detection and correction, data transmission and data storage. Codes are studied by various scientific disciplines—such as information theory, electrical engineering, mathematics, linguistics, and computer science—for the purpose of designing efficient and reliable data transmission methods.
Decoding methodsIn coding theory, decoding is the process of translating received messages into codewords of a given code. There have been many common methods of mapping messages to codewords. These are often used to recover messages sent over a noisy channel, such as a binary symmetric channel. is considered a binary code with the length ; shall be elements of ; and is the distance between those elements. One may be given the message , then ideal observer decoding generates the codeword .
Data compressionIn information theory, data compression, source coding, or bit-rate reduction is the process of encoding information using fewer bits than the original representation. Any particular compression is either lossy or lossless. Lossless compression reduces bits by identifying and eliminating statistical redundancy. No information is lost in lossless compression. Lossy compression reduces bits by removing unnecessary or less important information.
Lossless compressionLossless compression is a class of data compression that allows the original data to be perfectly reconstructed from the compressed data with no loss of information. Lossless compression is possible because most real-world data exhibits statistical redundancy. By contrast, lossy compression permits reconstruction only of an approximation of the original data, though usually with greatly improved compression rates (and therefore reduced media sizes).
Lossy compressionIn information technology, lossy compression or irreversible compression is the class of data compression methods that uses inexact approximations and partial data discarding to represent the content. These techniques are used to reduce data size for storing, handling, and transmitting content. The different versions of the photo of the cat on this page show how higher degrees of approximation create coarser images as more details are removed. This is opposed to lossless data compression (reversible data compression) which does not degrade the data.
Video codecA video codec is software or hardware that compresses and decompresses digital video. In the context of video compression, codec is a portmanteau of encoder and decoder, while a device that only compresses is typically called an encoder, and one that only decompresses is a decoder. The compressed data format usually conforms to a standard video coding format. The compression is typically lossy, meaning that the compressed video lacks some information present in the original video.
Video coding formatA video coding format (or sometimes video compression format) is a content representation format for storage or transmission of digital video content (such as in a data file or bitstream). It typically uses a standardized video compression algorithm, most commonly based on discrete cosine transform (DCT) coding and motion compensation. A specific software, firmware, or hardware implementation capable of compression or decompression to/from a specific video coding format is called a video codec.
Image compressionImage compression is a type of data compression applied to s, to reduce their cost for storage or transmission. Algorithms may take advantage of visual perception and the statistical properties of image data to provide superior results compared with generic data compression methods which are used for other digital data. Image compression may be lossy or lossless. Lossless compression is preferred for archival purposes and often for medical imaging, technical drawings, clip art, or comics.
Compression artifactA compression artifact (or artefact) is a noticeable distortion of media (including , audio, and video) caused by the application of lossy compression. Lossy data compression involves discarding some of the media's data so that it becomes small enough to be stored within the desired or transmitted (streamed) within the available bandwidth (known as the data rate or bit rate). If the compressor cannot store enough data in the compressed version, the result is a loss of quality, or introduction of artifacts.
Huffman codingIn computer science and information theory, a Huffman code is a particular type of optimal prefix code that is commonly used for lossless data compression. The process of finding or using such a code is Huffman coding, an algorithm developed by David A. Huffman while he was a Sc.D. student at MIT, and published in the 1952 paper "A Method for the Construction of Minimum-Redundancy Codes". The output from Huffman's algorithm can be viewed as a variable-length code table for encoding a source symbol (such as a character in a file).
Low-density parity-check codeIn information theory, a low-density parity-check (LDPC) code is a linear error correcting code, a method of transmitting a message over a noisy transmission channel. An LDPC code is constructed using a sparse Tanner graph (subclass of the bipartite graph). LDPC codes are , which means that practical constructions exist that allow the noise threshold to be set very close to the theoretical maximum (the Shannon limit) for a symmetric memoryless channel.
Entropy codingIn information theory, an entropy coding (or entropy encoding) is any lossless data compression method that attempts to approach the lower bound declared by Shannon's source coding theorem, which states that any lossless data compression method must have expected code length greater or equal to the entropy of the source. More precisely, the source coding theorem states that for any source distribution, the expected code length satisfies , where is the number of symbols in a code word, is the coding function, is the number of symbols used to make output codes and is the probability of the source symbol.
Block codeIn coding theory, block codes are a large and important family of error-correcting codes that encode data in blocks. There is a vast number of examples for block codes, many of which have a wide range of practical applications. The abstract definition of block codes is conceptually useful because it allows coding theorists, mathematicians, and computer scientists to study the limitations of all block codes in a unified way.
Linear network codingIn computer networking, linear network coding is a program in which intermediate nodes transmit data from source nodes to sink nodes by means of linear combinations. Linear network coding may be used to improve a network's throughput, efficiency, and scalability, as well as reducing attacks and eavesdropping. The nodes of a network take several packets and combine for transmission. This process may be used to attain the maximum possible information flow in a network.
Speech codingSpeech coding is an application of data compression to digital audio signals containing speech. Speech coding uses speech-specific parameter estimation using audio signal processing techniques to model the speech signal, combined with generic data compression algorithms to represent the resulting modeled parameters in a compact bitstream. Common applications of speech coding are mobile telephony and voice over IP (VoIP).
Communication channelA communication channel refers either to a physical transmission medium such as a wire, or to a logical connection over a multiplexed medium such as a radio channel in telecommunications and computer networking. A channel is used for information transfer of, for example, a digital bit stream, from one or several senders to one or several receivers. A channel has a certain capacity for transmitting information, often measured by its bandwidth in Hz or its data rate in bits per second.
Cyclic codeIn coding theory, a cyclic code is a block code, where the circular shifts of each codeword gives another word that belongs to the code. They are error-correcting codes that have algebraic properties that are convenient for efficient error detection and correction. Let be a linear code over a finite field (also called Galois field) of block length . is called a cyclic code if, for every codeword from , the word in obtained by a cyclic right shift of components is again a codeword.
Line codeIn telecommunication, a line code is a pattern of voltage, current, or photons used to represent digital data transmitted down a communication channel or written to a storage medium. This repertoire of signals is usually called a constrained code in data storage systems. Some signals are more prone to error than others as the physics of the communication channel or storage medium constrains the repertoire of signals that can be used reliably. Common line encodings are unipolar, polar, bipolar, and Manchester code.
Viterbi decoderA Viterbi decoder uses the Viterbi algorithm for decoding a bitstream that has been encoded using a convolutional code or trellis code. There are other algorithms for decoding a convolutionally encoded stream (for example, the Fano algorithm). The Viterbi algorithm is the most resource-consuming, but it does the maximum likelihood decoding. It is most often used for decoding convolutional codes with constraint lengths k≤3, but values up to k=15 are used in practice. Viterbi decoding was developed by Andrew J.
