Superposition codes and approximate-message-passing decoder

Superposition codes are asymptotically capacity achieving scheme for the Additive White Gaussian Noise channel. I will first show how a practical iterative decoder can be built based on a Belief Propagation type approach, closely related to the one performed in compressed sensing and sparse estimation problems. Secondly, I will show how the idea of spatial coupling in this context allows to built efficient and practical capacity achieving coding and decoding schemes. The links between the present problem, sparse estimations, and non-parametric belief propagation for continuous variables will be also discussed.
References:
Replica Analysis and Approximate Message Passing Decoder for Superposition Codes, J. Barbier and F. Krzakala, ISIT 2014.
Statistical physics-based reconstruction in compressed sensing, F. Krzakala et al. Phys. Rev. X 2, 021005 (2012)