Smooth compression, Gallager bound and nonlinear sparse-graph codes

A data compression scheme is defined to be smooth if its image (the codeword) depends gracefully on the source (the data). Smoothness is a desirable property in many practical contexts, and widely used source coding schemes lack of it. We introduce a family of smooth source codes based on sparse graph constructions, and prove them to achieve the (information theoretic) optimal compression rate for a dense set of iid sources. As a byproduct, we show how Gallager bound on sparsity can be overcome using non-linear function nodes.