On Burst Error Correction and Storage Security of Noisy Data

Secure storage of noisy data for authentication purposes usually involves the use of error correcting codes. We propose a new model scenario involving burst errors and present for that several constructions.Comment: to be presented at MTNS 201

How to correct small quantum errors

The theory of quantum error correction is a cornerstone of quantum information processing. It shows that quantum data can be protected against decoherence effects, which otherwise would render many of the new quantum applications practically impossible. In this paper we give a self contained introduction to this theory and to the closely related concept of quantum channel capacities. We show, in particular, that it is possible (using appropriate error correcting schemes) to send a non-vanishing amount of quantum data undisturbed (in a certain asymptotic sense) through a noisy quantum channel T, provided the errors produced by T are small enough.Comment: LaTeX2e, 23 pages, 6 figures (3 eps, 3 pstricks

Reconstruction Codes for DNA Sequences with Uniform Tandem-Duplication Errors

DNA as a data storage medium has several advantages, including far greater data density compared to electronic media. We propose that schemes for data storage in the DNA of living organisms may benefit from studying the reconstruction problem, which is applicable whenever multiple reads of noisy data are available. This strategy is uniquely suited to the medium, which inherently replicates stored data in multiple distinct ways, caused by mutations. We consider noise introduced solely by uniform tandem-duplication, and utilize the relation to constant-weight integer codes in the Manhattan metric. By bounding the intersection of the cross-polytope with hyperplanes, we prove the existence of reconstruction codes with greater capacity than known error-correcting codes, which we can determine analytically for any set of parameters.Comment: 11 pages, 2 figures, Latex; version accepted for publicatio

Diurnal measurements with prototype CMOS Omega receivers

Diurnal signals from eight omega channels have been monitored at 10.2 KHz for selected station pairs. All eight Omega stations have been received at least 50 percent of the time over a 24 hour period during the month of October 1976. The data presented confirm the expected performance of the CMOS omega sensor processor in being able to digsignals out of a noisy environment. Of particular interest are possibilities for use of antipodal reception phenomena and a need for some ways of correcting for multi-modal propagation effects

CodNN – Robust Neural Networks From Coded Classification

Deep Neural Networks (DNNs) are a revolutionary force in the ongoing information revolution, and yet their intrinsic properties remain a mystery. In particular, it is widely known that DNNs are highly sensitive to noise, whether adversarial or random. This poses a fundamental challenge for hardware implementations of DNNs, and for their deployment in critical applications such as autonomous driving.In this paper we construct robust DNNs via error correcting codes. By our approach, either the data or internal layers of the DNN are coded with error correcting codes, and successful computation under noise is guaranteed. Since DNNs can be seen as a layered concatenation of classification tasks, our research begins with the core task of classifying noisy coded inputs, and progresses towards robust DNNs.We focus on binary data and linear codes. Our main result is that the prevalent parity code can guarantee robustness for a large family of DNNs, which includes the recently popularized binarized neural networks. Further, we show that the coded classification problem has a deep connection to Fourier analysis of Boolean functions.In contrast to existing solutions in the literature, our results do not rely on altering the training process of the DNN, and provide mathematically rigorous guarantees rather than experimental evidence