This thesis studies a neural network inspired by human neocortex. An extension of the recurrent and binary network proposed by Gripon and Berrou is given to store sparse messages. In this new version of the neural network, information is borne by graphical codewords (cliques) that use a fraction of the network available resources. These codewords can have different sizes that carry variable length information. We have examined this concept and computed the capacity limits on erasure correction as a function of error rate. These limits are compared with simulation results that are obtained from different experiment setups. We have finally studied the network under the formalism of information theory and established a connection between compressed sensing and the proposed network.