Turbo Analog Error Correcting Codes Decodable By Linear Programming

TL;DR

This paper introduces a Turbo analog error correcting code for real signals corrupted by impulsive noise, utilizing probabilistic methods and linear programming to enhance error correction and reduce decoding complexity.

Contribution

It presents a novel Turbo coding scheme that improves error correction over Donoho's deterministic matrices by employing probabilistic design and parallel linear programming decoding.

Findings

Corrects more errors than Donoho's matrices with high probability

Decouples decoding into parallel LP problems for efficiency

Reduces decoding complexity significantly

Abstract

In this paper we present a new Turbo analog error correcting coding scheme for real valued signals that are corrupted by impulsive noise. This Turbo code improves Donoho's deterministic construction by using a probabilistic approach. More specifically, our construction corrects more errors than the matrices of Donoho 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.