We consider the estimation of a signal from knowledge its noisy linear random Gaussian projections, problem relevant in compressed sensing, sparse superposition codes or code division multiple access just to cite few. There has been number works considering mutual information for this using heuristic replica method statistical physics. Here we put these considerations on firm rigorous basis. First, show, Guerra-type interpolation, that formula yields an upper bound exact information....

Factorizing low-rank matrices has many applications in machine learning and statistics. For probabilistic models the Bayes optimal setting, a general expression for mutual information been proposed using heuristic statistical physics computations, proven few specific cases. Here, we show how to rigorously prove conjectured formula symmetric rank-one case. This allows express minimal mean-square-error characterize detectability phase transitions large set of estimation problems ranging from...

We consider the estimation of a signal from knowledge its noisy linear random Gaussian projections. A few examples where this problem is relevant are compressed sensing, sparse superposition codes, and code division multiple access. There has been number works considering mutual information for using replica method statistical physics. Here we put these considerations on firm rigorous basis. First, show, Guerra-Toninelli type interpolation, that formula yields an upper bound to exact...

Recently, a new class of codes, called sparse superposition or regression has been proposed for communication over the AWGN channel. It proven that they achieve capacity using power allocation and various forms iterative decoding. Empirical evidence also strongly suggested codes when spatial coupling approximate message passing decoding are used, without need allocation. In this note we prove state evolution (which tracks passing) indeed saturates potential threshold underlying code...

Sparse superposition codes, or sparse regression constitute a new class of which was first introduced for communication over the additive white Gaussian noise (AWGN) channel. It has been shown that such codes are capacity-achieving AWGN channel under optimal maximum-likelihood decoding as well various efficient iterative schemes equipped with power allocation spatially coupled constructions. Here, we generalize analysis these to much broader setting includes all memoryless channels. We show,...

We recently proved threshold saturation for spatially coupled sparse superposition codes on the additive white Gaussian noise channel [1]. Here we generalize our analysis to a much broader setting. show any memoryless that spatial coupling allows generalized approximate message-passing (GAMP) decoding reach potential (or Bayes optimal) of code ensemble. Moreover in large input alphabet size limit: i) GAMP algorithmic underlying uncoupled) ensemble is simply expressed as Fisher information;...

Factorizing low-rank matrices is a problem with many applications in machine learning and statistics, ranging from sparse PCA to community detection sub-matrix localization. For probabilistic models the Bayes optimal setting, general expressions for mutual information have been proposed using powerful heuristic statistical physics computations via replica cavity methods, proven few specific cases by variety of methods. Here, we use spatial coupling methodology developed framework error...

In this paper, we consider the design of 3G/WiFi heterogeneous networks under realistic operational conditions. The aim is reduce energy consumed from batteries on mobile devices by utilizing multiple available wireless interfaces and dynamically switching between 3G WiFi. We conduct a set experimental measurements in various network scenarios order to identify main components that impact consumption while connected WiFi networks. measurement results are then used derive generic analytical...

In this work, we provide an efficient and realistic data-driven approach to simulate astronomical images using deep generative models from machine learning. Our solution is based on a variant of the adversarial network (GAN) with progressive training methodology Wasserstein cost function. The proposed generates naturalistic galaxies that show complex structures high diversity, which suggests simulations learning can replace many expensive model-driven methods used in data processing.

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 are universal, in sense they achieve capacity any memoryless under generalized approximate message-passing (GAMP) decoding [2], although this decoder has never been stated for SS codes. In contribution we introduce GAMP codes, confirm empirically universality of through its study on...

Sparse superposition codes, or sparse regression constitute a new class of codes which was first introduced for communication over the additive white Gaussian noise (AWGN) channel. It has been shown that such are capacity-achieving AWGN channel under optimal maximum-likelihood decoding as well various efficient iterative schemes equipped with power allocation spatially coupled constructions. Here, we generalize analysis these to much broader setting includes all memoryless channels. We show,...

In this work, we formulate the fixed-length distribution matching as a Bayesian inference problem. Our proposed solution is inspired from compressed sensing paradigm and sparse superposition (SS) codes. First, introduce sparsity in binary source via position modulation (PM). We then present simple exact matcher based on Gaussian signal quantization. At receiver, dematcher exploits performs low-complexity dematching generalized approximate message-passing (GAMP). show that GAMP spatial...

We recently proved threshold saturation for spatially coupled sparse superposition codes on the additive white Gaussian noise channel. Here we generalize our analysis to a much broader setting. show any memoryless channel that spatial coupling allows generalized approximate message-passing (GAMP) decoding reach potential (or Bayes optimal) of code ensemble. Moreover in large input alphabet size limit: i) GAMP algorithmic underlying uncoupled) ensemble is simply expressed as Fisher...

Recently, a new class of codes, called sparse superposition or regression has been proposed for communication over the AWGN channel. It proven that they achieve capacity using power allocation and various forms iterative decoding. Empirical evidence also strongly suggested codes when spatial coupling approximate message passing decoding are used, without need allocation. In this note we prove state evolution (which tracks passing) indeed saturates potential threshold underlying code...

In this work, we formulate the fixed-length distribution matching as a Bayesian inference problem. Our proposed solution is inspired from compressed sensing paradigm and sparse superposition (SS) codes. First, introduce sparsity in binary source via position modulation (PM). We then present simple exact matcher based on Gaussian signal quantization. At receiver, dematcher exploits performs low-complexity dematching generalized approximate message-passing (GAMP). show that GAMP spatial...