A Sparse graph code is a

code In communications and information processing, code is a system of rules to convert information—such as a letter, word, sound, image, or gesture—into another form, sometimes shortened or secret, for communication through a communication ...

which is represented by a

sparse graph In mathematics, a dense graph is a graph in which the number of edges is close to the maximal number of edges (where every pair of vertices is connected by one edge). The opposite, a graph with only a few edges, is a sparse graph. The distinction ...

. Any

linear code In coding theory, a linear code is an error-correcting code for which any linear combination of codewords is also a codeword. Linear codes are traditionally partitioned into block codes and convolutional codes, although turbo codes can be seen as ...

can be represented as a graph, where there are two sets of nodes - a set representing the transmitted

bit The bit is the most basic unit of information in computing and digital communications. The name is a portmanteau of binary digit. The bit represents a logical state with one of two possible values. These values are most commonly represente ...

s and another set representing the constraints that the transmitted bits have to satisfy. The state of the art classical

error-correcting code In computing, telecommunication, information theory, and coding theory, an error correction code, sometimes error correcting code, (ECC) is used for controlling errors in data over unreliable or noisy communication channels. The central idea is ...

s are based on sparse graphs, achieving close to the

Shannon limit In information theory, the noisy-channel coding theorem (sometimes Shannon's theorem or Shannon's limit), establishes that for any given degree of noise contamination of a communication channel, it is possible to communicate discrete data (di ...

. The archetypal sparse-graph codes are Gallager's low-density parity-check codes.

External links

The on-line textbook: Information Theory, Inference, and Learning Algorithms
by

David J.C. MacKay Professor Sir David John Cameron MacKay (22 April 1967 – 14 April 2016) was a British physicist, mathematician, and academic. He was the Regius Professor of Engineering in the Department of Engineering at the University of Cambridge and fro ...

, discusses sparse-graph codes in Chapters 47–50.
Encyclopedia of Sparse Graph Codes

Iterative Error Correction: Turbo, Low-Density Parity-Check, and Repeat-Cccumulate Codes
Matrix theory Error detection and correction