Related papers: Error-Correcting Codes for Two Bursts of t1-Deleti…
Erasure coding techniques are used to increase the reliability of distributed storage systems while minimizing storage overhead. Also of interest is minimization of the bandwidth required to repair the system following a node failure. In a…
Topological error correction codes are promising candidates to protect quantum computations from the deteriorating effects of noise. While some codes provide high noise thresholds suitable for robust quantum memories, others allow…
Encoding data as a set of unordered strings is receiving great attention as it captures one of the basic features of DNA storage systems. However, the challenge of constructing optimal redundancy codes for this channel remained elusive. In…
This manuscript presents a construction method for quantum codes capable of correcting multiple deletion errors. By introducing two new alogorithms, the alternating sandwich mapping and the block error locator, the proposed method reduces…
Quantum error correction/detection (QEC/QED) and dynamical decoupling (DD) are tools for protecting quantum information. A natural goal is to combine them to outperform either approach alone. Such a benefit is not automatic: physical DD can…
Storing digital data in synthetic DNA faces challenges in ensuring data reliability in the presence of edit errors--deletions, insertions, and substitutions--that occur randomly during various stages of the storage process. Current…
Recent progress in quantum computing has enabled systems with tens of reliable logical qubits, built from thousands of noisy physical qubits. However, many impactful applications demand quantum computations with millions of logical qubits,…
Quantum error correction (QEC) codes are traditionally defined and searched for without specifying the manner in which its syndrome extraction circuits are executed using elementary gates and measurements. We show how morphing circuits…
Nanopore sequencers are emerging as promising new platforms for high-throughput sequencing. As with other technologies, sequencer errors pose a major challenge for their effective use. In this paper, we present a novel information theoretic…
State-of-the-art techniques for addressing scaling-related main memory errors identify and repair bits that are at risk of error from within the memory controller. Unfortunately, modern main memory chips internally use on-die error…
In this work, we introduce convolutional codes for network-error correction in the context of coherent network coding. We give a construction of convolutional codes that correct a given set of error patterns, as long as consecutive errors…
We propose a two-layer coding architecture for communication of multiple users over a shared slotted medium enabling joint collision resolution and decoding. Each user first encodes its information bits with an outer code for reliability,…
We construct new families of multi-error-correcting quantum codes for the amplitude damping channel. Our key observation is that, with proper encoding, two uses of the amplitude damping channel simulate a quantum erasure channel. This…
Tandem duplication is the process of inserting a copy of a segment of DNA adjacent to the original position. Motivated by applications that store data in living organisms, Jain et al. (2017) proposed the study of codes that correct tandem…
In this work, we study linear error-correcting codes against adversarial insertion-deletion (indel) errors. While most constructions for the indel model are nonlinear, linear codes offer compact representations, efficient encoding, and…
In this paper, we investigate binary reconstruction codes capable of correcting one deletion and one substitution. We define the \emph{single-deletion single-substitution ball} function $ \mathcal{B} $ as a mapping from a sequence to the…
Density evolution for protograph Low-Density Parity-Check (LDPC) codes is considered, and it is shown that the message-error rate falls double-exponentially with iterations whenever the degree-2 subgraph of the protograph is cycle-free and…
Non-binary codes correcting multiple deletions have recently attracted a lot of attention. In this work, we focus on multiplicity-free codes, a family of non-binary codes where all symbols are distinct. Our main contribution is a new…
Errors are inevitable during all kinds quantum informational tasks and quantum error-correcting codes (QECCs) are powerful tools to fight various quantum noises. For standard QECCs physical systems have the same number of energy levels.…
We propose a fault-tolerant quantum error correction architecture consisting of a linear array of emitters and delay lines. In our scheme, a resource state for fault-tolerant quantum computation is generated by letting the emitters interact…