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Approximate message passing (AMP) is a class of efficient algorithms for solving high-dimensional linear regression tasks where one wishes to recover an unknown signal βο from noisy, linear measurements y = Αβ0 + w. When applying a separable denoiser at each iteration, the performance of AMP (for example, the mean squared error of its estimates) can be accurately tracked by a simple, scalar iteration...
Sparse regression codes (SPARCs) are a recent class of codes for reliable communication over the AWGN channel at rates approaching the channel capacity. Approximate message passing (AMP) decoding, a computationally efficient technique for decoding SPARCs, has been proven to be asymptotically capacity-achieving for the AWGN channel. In this paper, we refine the asymptotic results by deriving a large...
Sparse superposition codes were recently introduced by Barron and Joseph for reliable communication over the additive white Gaussian noise (AWGN) channel at rates approaching the channel capacity. The codebook is defined in terms of a Gaussian design matrix, and codewords are sparse linear combinations of columns of the matrix. In this paper, we propose an approximate message passing decoder for sparse...
This paper studies the performance of Approximate Message Passing (AMP), in the regime where the problem dimension is large but finite. We consider the setting of high-dimensional regression, where the goal is to estimate a high-dimensional vector β0 from an observation y = Aβ0 + w. AMP is a low-complexity, scalable algorithm for this problem. It has the attractive feature that its performance can...
Sparse superposition codes were recently introduced by Barron and Joseph for reliable communication over the AWGN channel at rates approaching the channel capacity. In this code, the codewords are sparse linear combinations of columns of a design matrix. In this paper, we propose an approximate message passing decoder for sparse superposition codes. The complexity of the decoder scales linearly with...
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