Replica Analysis and Approximate Message Passing Decoder for Superposition Codes

Superposition codes are efficient for the Additive White Gaussian Noise channel. We provide here a replica analysis of the performances of these codes for large signals. We also consider a Bayesian Approximate Message Passing decoder based on a belief-propagation approach, and discuss its performance using the density evolution technic. Our main findings are 1) for the sizes we can access, the message-passing decoder outperforms other decoders studied in the literature 2) its performance is limited by a sharp phase transition and 3) while these codes reach capacity as $B$ (a crucial parameter in the code) increases, the performance of the message passing decoder worsen as the phase transition goes to lower rates.Comment: 5 pages, 5 figures, To be presented at the 2014 IEEE International Symposium on Information Theor

The adaptive interpolation method for proving replica formulas. Applications to the Curie-Weiss and Wigner spike models

In this contribution we give a pedagogic introduction to the newly introduced adaptive interpolation method to prove in a simple and unified way replica formulas for Bayesian optimal inference problems. Many aspects of this method can already be explained at the level of the simple Curie-Weiss spin system. This provides a new method of solution for this model which does not appear to be known. We then generalize this analysis to a paradigmatic inference problem, namely rank-one matrix estimation, also refered to as the Wigner spike model in statistics. We give many pointers to the recent literature where the method has been succesfully applied

Generalized Approximate Message-Passing Decoder for Universal Sparse Superposition Codes

Sparse superposition (SS) codes were originally proposed as a capacity-achieving communication scheme over the additive white Gaussian noise channel (AWGNC) [1]. Very recently, it was discovered that these codes are universal, in the sense that they achieve capacity over any memoryless channel under generalized approximate message-passing (GAMP) decoding [2], although this decoder has never been stated for SS codes. In this contribution we introduce the GAMP decoder for SS codes, we confirm empirically the universality of this communication scheme through its study on various channels and we provide the main analysis tools: state evolution and potential. We also compare the performance of GAMP with the Bayes-optimal MMSE decoder. We empirically illustrate that despite the presence of a phase transition preventing GAMP to reach the optimal performance, spatial coupling allows to boost the performance that eventually tends to capacity in a proper limit. We also prove that, in contrast with the AWGNC case, SS codes for binary input channels have a vanishing error floor in the limit of large codewords. Moreover, the performance of Hadamard-based encoders is assessed for practical implementations

Of similarities and divergences : why there is no continental ideal-type of "activation reforms"

In matters of "activation of social protection" as in other policy areas, one would expect that three types of welfare regimes would be identifiable. However, with the hindsight of 20 years of the deployment of "activation strategies", it is still impossible to draw the stylized characters of a "Bismarckian" or " conservative-corporatist" type to compare with the Scandinavian and Liberal ones. In the domain, Germany and France have reformed, each with their own pace and timing, according to their institutional systems, systems of actors and political culture. They have much in common, but also persistent dissimilarities that can be ascribed to their long term history. The empirically detailed survey (from the 1960's) contributes to confirming that a "broad view" comparison leaves aside many crucial explanatory factors. It also shows the limits of an analysis in terms of welfare regimes, when it comes to explaining change and reform. Finally, both societies have implemented policies and reforms that have fostered an amazing fragmentation of situations, a much more complex situation that the simple opposition between "insiders" and "outsiders" is unable to capture, while it postulates a "dualization" of their social protection systems.Activating social protection, welfare, social protection, comparison France-Germany, Bismarckianism, welfare regimes.