Sparsity-Based Recovery of Finite Alphabet Solutions to Underdetermined Linear Systems


We consider the problem of estimating a deterministic finite alphabet vector $ f$ from underdetermined measurements $ y= A f $ , where $ A$ is a given (random) $n times N$ matrix. 2 new convex optimization ways are introduced for the recovery of finite alphabet signals via $ell _1$ -norm minimization. The first methodology is based on regularization. Within the second approach, the matter is formulated as the recovery of sparse signals when a appropriate sparse rework. The regularization-based mostly technique is a smaller amount complex than the transform-based one. When the alphabet size $p$ equals 2 and $(n,N)$ grows proportionally, the conditions underneath which the signal will be recovered with high chance are the identical for the 2 methods. When $p > a pair of$ , the behavior of the remodel-primarily based technique is established. Experimental results support this theoretical result and show that the rework technique outperforms the regularization-primarily based one.

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