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Recently, a lot of effort has been devoted towards designing erasure qubits in which dominant physical noise excites leakage states whose population can be detected and returned to the qubit subspace. Interest in these erasure qubits has…
Reed--Solomon error-correcting codes are ubiquitous across computer science and information theory, with applications in cryptography, computational complexity, communication and storage systems, and more. Most works on efficient error…
Atom loss is a dominant error source in neutral-atom quantum processors, yet its correlated structure remains largely unexploited by existing quantum error correction decoders. We analyze the performance of the surface code equipped with…
Product codes (PCs) protect a two-dimensional array of bits using short component codes. Assuming transmission over the binary symmetric channel, the decoding is commonly performed by iteratively applying bounded-distance decoding to the…
In the current thesis we first talk about the six-qubit quantum error-correcting code and show its connections to entanglement-assisted error-correcting coding theory and then to subsystem codes. This code bridges the gap between the…
Repetition code forms a fundamental basis for quantum error correction experiments. To date, it stands as the sole code that has achieved large distances and extremely low error rates. Its applications span the spectrum of evaluating…
We prove the following results concerning the list decoding of error-correcting codes: (i) We show that for \textit{any} code with a relative distance of $\delta$ (over a large enough alphabet), the following result holds for \textit{random…
Reed-Solomon (RS) codes are an important class of non-binary error-correction codes. They are particularly competent in correcting burst errors, being widely applied in modern communications and data storage systems. This also thanks to…
We address the challenge of incorporating encoded quantum memories into an exact secret key rate analysis for small and intermediate-scale quantum repeaters. To this end, we introduce the check matrix model and quantify the resilience of…
With the rapid developments in quantum hardware comes a push towards the first practical applications on these devices. While fully fault-tolerant quantum computers may still be years away, one may ask if there exist intermediate forms of…
We address the problem of decoding Gabidulin codes beyond their unique error-correction radius. The complexity of this problem is of importance to assess the security of some rank-metric code-based cryptosystems. We propose an approach that…
Practical storage systems often adopt erasure codes to tolerate device failures and sector failures, both of which are prevalent in the field. However, traditional erasure codes employ device-level redundancy to protect against sector…
Quantum error correction is a set of methods to protect quantum information--that is, quantum states--from unwanted environmental interactions (decoherence) and other forms of noise. The information is stored in a quantum error-correcting…
This paper presents and analyzes a novel concatenated coding scheme for enabling error resilience in two distributed storage settings: one being storage using existing regenerating codes and the second being storage using locally repairable…
In recent years, neural networks have become the default choice for image classification and many other learning tasks, even though they are vulnerable to so-called adversarial attacks. To increase their robustness against these attacks,…
Reliability is an important requirement for both communication and storage systems. Due to continuous scale down of technology multiple adjacent bits error probability increases. The data may be corrupted due soft errors. Error correction…
Quantum computers hold the promise of solving computational problems which are intractable using conventional methods. For fault-tolerant operation quantum computers must correct errors occurring due to unavoidable decoherence and limited…
Matrix multiplication over the real field constitutes a foundational operation in the training of deep learning models, serving as a computational cornerstone for both forward and backward propagation processes. However, the presence of…
In this paper, we revisit traditional checkpointing and rollback recovery strategies, with a focus on silent data corruption errors. Contrarily to fail-stop failures, such latent errors cannot be detected immediately, and a mechanism to…
Leakage is a particularly damaging error that occurs when a qubit state falls out of its two-level computational subspace. Compared to independent depolarizing noise, leaked qubits may produce many more configurations of harmful correlated…