Robust Bayesian compressed sensing over finite fields: asymptotic performance analysis

TL;DR

This paper analyzes the asymptotic performance of robust Bayesian compressed sensing over finite fields, establishing conditions on measurements and sensing matrix sparsity for accurate reconstruction under noise.

Contribution

It provides necessary and sufficient asymptotic conditions for measurement requirements in noisy finite field compressed sensing, extending previous results.

Findings

Necessary and sufficient measurement conditions are derived.

Sparsity conditions on sensing matrices are established.

Results generalize and extend prior work on noisy compressed sensing.

Abstract

This paper addresses the topic of robust Bayesian compressed sensing over finite fields. For stationary and ergodic sources, it provides asymptotic (with the size of the vector to estimate) necessary and sufficient conditions on the number of required measurements to achieve vanishing reconstruction error, in presence of sensing and communication noise. In all considered cases, the necessary and sufficient conditions asymptotically coincide. Conditions on the sparsity of the sensing matrix are established in presence of communication noise. Several previously published results are generalized and extended.