A Sparse graph code is a code

Code

A code is a rule for converting a piece of information into another form or representation , not necessarily of the same type....

 which is represented by a sparse graph.

Any linear code

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 a hybrid of these two types. Linear codes allow for...

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

Bit

A bit is the basic unit of information in computing and telecommunications; it is the amount of information stored by a digital device or other physical system that exists in one of two possible distinct states...

s and another set representing the constraints that the transmitted bits have to satisfy. The state of the art classical error-correcting codes are based on sparse graphs, achieving close to the Shannon limit. The archetypal sparse-graph codes are Gallager's

Robert G. Gallager

Robert Gray Gallager is an American electrical engineer known for his work on information theory and communications networks. He was elected an IEEE Fellow in 1968 and a member of the National Academy of Engineering in 1979. He received the Claude E. Shannon Award from the IEEE Information Theory...

 low-density parity-check code

Low-density parity-check code

In information theory, a low-density parity-check code is a linear error correcting code, a method of transmitting a message over a noisy transmission channel, and is constructed using a sparse bipartite graph...

s.

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
• Iterative Error Correction: Turbo, Low-Density Parity-Check, and Repeat-Cccumulate Codes