A Sparse graph code is a code which is represented by a sparse graph. In Communications a code is a rule for converting a piece of Information (for example a letter, Word, Phrase, or In Mathematics, a dense graph is a graph in which the number of edges is close to the maximal number of edges
Any linear code can be represented as a graph, where there are two sets of nodes - a set representing the transmitted bits and another set representing the constraints that the transmitted bits have to satisfy. In Mathematics and Information theory, a linear code is an important type of Block code used in Error correction and detection schemes A bit is a binary digit, taking a value of either 0 or 1 Binary digits are a basic unit of Information storage and communication The state of the art classical error-correcting codes are based on sparse graphs, achieving close to the Shannon limit. In Telecommunication and Information theory, forward error correction (FEC is a System of Error control for Data transmission, whereby In Information theory, the noisy-channel coding theorem establishes that however contaminated with noise interference a communication channel may be it is possible to communicate The archetypal sparse-graph codes are Gallager's low-density parity-check codes. Robert G Gallager (born May 29, 1931 in Philadelphia PA) is an American electrical engineer known for his work on Information theory In Information theory, a low-density parity-check code (LDPC code is an Error correcting code, a method of transmitting a message over a noisy transmission
External links
- The on-line textbook: Information Theory, Inference, and Learning Algorithms, by David J.C. MacKay, discusses sparse-graph codes in Chapters 47-50.
- Encyclopedia of Sparse Graph Codes
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