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In this paper, we present a new analog error correcting coding scheme for real valued signals that are corrupted by impulsive noise. This product code improves Donoho's deterministic construction by using a probabilistic approach. More specifically, our construction corrects more errors than the Donoho matrices by allowing a vanishingly small probability of error (with the increase in block size). The problem of decoding the long block code is decoupled into two sets of parallel Linear Programming problems. This leads to a significant reduction in decoding complexity as compared to one-step Linear Programming decoding.