Sparse graph code

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 constrains that the transmitted bits have to satisfy. A Sparse graph code is a code where the graph that represents it is sparse. The state of the art classical error-correcting codes are based on sparse graphs, achieving closely the Nyquist-Shannon limits. The archetypal sparse-graph codes are Gallager's low-density parity-check codes.