On Compressive Sensing in Coding Problems: A Rigorous Approach

Wasim Huleihel; Neri Merhav; Shlomo Shamai

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arXiv · 1403.5874

On Compressive Sensing in Coding Problems: A Rigorous Approach

Wasim Huleihel·Neri Merhav·Shlomo Shamai

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Abstract

We take an information theoretic perspective on a classical sparse-sampling noisy linear model and present an analytical expression for the mutual information, which plays central role in a variety of communications/processing problems. Such an expression was addressed previously either by bounds, by simulations and by the (non-rigorous) replica method. The expression of the mutual information is based on techniques used in [1], addressing the minimum mean square error (MMSE) analysis. Using these expressions, we study specifically a variety of sparse linear communications models which include coding in different settings, accounting also for multiple access channels and different wiretap problems. For those, we provide single-letter expressions and derive achievable rates, capturing the communications/processing features of these timely models.

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Wasim Huleihel, Neri Merhav, Shlomo Shamai. 2014-03-24. On Compressive Sensing in Coding Problems: A Rigorous Approach. https://arxiv.org/abs/1403.5874

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