Related papers: Coding for Polymer-Based Data Storage
Linear nested codes, where two or more sub-codes are nested in a global code, have been proposed as candidates for reliable multi-terminal communication. In this paper, we consider nested array-based spatially coupled low-density…
We study the two-dimensional hierarchical rectangle packing problem, motivated by applications in analog integrated circuit layout, facility layout, and logistics. Unlike classical strip or bin packing, the dimensions of the container are…
The strongly correlated systems we use to realise quantum error-correcting codes may give rise to high-weight, problematic errors. Encouragingly, we can expect local quantum error-correcting codes with no string-like logical operators $-$…
Polynomial, or Delsarte's, method in coding theory accounts for a variety of structural results on, and bounds on the size of, extremal configurations (codes and designs) in various metric spaces. In recent works of the authors the…
Quantifying material mass and electron density from computed tomography (CT) reconstructions can be highly valuable in certain medical practices, such as radiation therapy planning. However, uniquely parameterising the X-ray attenuation in…
The construction of asymmetric error correcting codes is a topic that was studied extensively, however, the existing approach for code construction assumes that every codeword should tolerate $t$ asymmetric errors. Our main observation is…
This paper studies the fundamental problem of data persistency for a general family of redundancy schemes in distributed storage systems, called replicated erasure codes. Namely, we analyze two strategies of replicated erasure codes…
Binary measurements arise naturally in a variety of statistical and engineering applications. They may be inherent to the problem---e.g., in determining the relationship between genetics and the presence or absence of a disease---or they…
Error-correcting codes are a method for representing data, so that one can recover the original information even if some parts of it were corrupted. The basic idea, which dates back to the revolutionary work of Shannon and Hamming about a…
The paper is devoted to the problem of erasure coding in distributed storage. We consider a model of storage that assumes that nodes are organized into equally sized groups, called racks, that within each group the nodes can communicate…
In the age of data revolution, a modern storage~or transmission system typically requires different levels of protection. For example, the coding technique used to fortify data in a modern storage system when the device is fresh cannot be…
Ordered statistics decoding has been instrumental in addressing decoding failures that persist after normalized min-sum decoding in short low-density parity-check codes. Despite its benefits, the high computational complexity of effective…
Symmetric tensor operations arise in a wide variety of computations. However, the benefits of exploiting symmetry in order to reduce storage and computation is in conflict with a desire to simplify memory access patterns. In this paper, we…
Product codes are a concatenated error-correction scheme that has been often considered for applications requiring very low bit-error rates, which demand that the error floor be decreased as much as possible. In this work, we consider…
Recursive list decoding of Reed-Muller (RM) codes, with moderate list size, is known to approach maximum-likelihood (ML) performance of short length $(\leq 256)$ RM codes. Recursive decoding employs the Plotkin construction to split the…
The sum-rank metric generalizes the Hamming and rank metric by partitioning vectors into blocks and defining the total weight as the sum of the rank weights of these blocks, based on their matrix representation. In this work, we explore…
Error correcting codes play a central role in digital communication, ensuring that transmitted information can be accurately reconstructed despite channel impairments. Recently, autoencoder (AE) based approaches have gained attention for…
Three-dimensional (3D) printing's accessibility enables rapid manufacturing but also poses security risks, such as the unauthorized production of untraceable firearms and prohibited items. To ensure traceability and accountability,…
We consider the numerical irreducible decomposition of a positive dimensional solution set of a polynomial system into irreducible factors. Path tracking techniques computing loops around singularities connect points on the same irreducible…
We study the theoretical performance of a combined approach to demodulation and decoding of binary continuous-phase modulated signals under repetition-like codes. This technique is motivated by a need to transmit packetized or framed data…