Sparse graph code

A Sparse graph code is a code for which the graph that represents it is sparse.

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. The state of the art classical error-correcting codes are based on sparse graphs, achieving close to the Nyquist-Shannon limits. The archetypal sparse-graph codes are Gallager's low-density parity-check codes.

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