Related papers: Coding for Polymer-Based Data Storage
The problem of string reconstruction based on its substrings spectrum has received significant attention recently due to its applicability to DNA data storage and sequencing. In contrast to previous works, we consider in this paper a setup…
We describe a strategy for constructing codes for DNA-based information storage by serial composition of weighted finite-state transducers. The resulting state machines can integrate correction of substitution errors; synchronization by…
In DNA-based data storage, DNA codes with biochemical constraints and error correction are designed to protect data reliability. Single-stranded DNA sequences with secondary structure avoidance (SSA) help to avoid undesirable secondary…
New soft- and hard decision decoding algorithms are presented for general Reed-Muller codes $\left\{\genfrac{}{}{0pt}{}{m}{r}\right\} $ of length $2^{m}$ and distance $2^{m-r}$. We use Plotkin $(u,u+v)$ construction and decompose code…
In this paper, we introduce a new coding and decoding structure for enhancing the reliability and performance of polar codes, specifically at low error rates. We achieve this by concatenating two polar codes in series to create robust…
Regenerating codes provide an efficient way to recover data at failed nodes in distributed storage systems. It has been shown that regenerating codes can be designed to minimize the per-node storage (called MSR) or minimize the…
A method for concatenating quantum error-correcting codes is presented. The method is applicable to a wide class of quantum error-correcting codes known as Calderbank-Shor-Steane (CSS) codes. As a result, codes that achieve a high rate in…
Constrained codes are used to prevent errors from occurring in various data storage and data transmission systems. They can help in increasing the storage density of magnetic storage devices, in managing the lifetime of electronic storage…
Distributed storage systems need to store data redundantly in order to provide some fault-tolerance and guarantee system reliability. Different coding techniques have been proposed to provide the required redundancy more efficiently than…
Quantum error-correcting codes with good parameters can be constructed by evaluating polynomials at the roots of the polynomial trace. In this paper, we propose to evaluate polynomials at the roots of trace-depending polynomials (given by a…
We consider a large-scale matrix multiplication problem where the computation is carried out using a distributed system with a master node and multiple worker nodes, where each worker can store parts of the input matrices. We propose a…
DNA synthesis is considered as one of the most expensive components in current DNA storage systems. In this paper, focusing on a common synthesis machine, which generates multiple DNA strands in parallel following a fixed supersequence,we…
This work provides an algebraic framework for source coding with decoder side information and its dual problem, channel coding with encoder side information, showing that nested concatenated codes can achieve the corresponding…
We address an open problem posed by Chen-Cheng-Qi (IEEE Trans.\ Inf.\ Theory, 2025): can the decoding of binary sum-rank-metric codes $\SR(C_1,C_2)$ with $2\times2$ matrix blocks be reduced entirely to decoding the constituent…
Erasure coding techniques are getting integrated in networked distributed storage systems as a way to provide fault-tolerance at the cost of less storage overhead than traditional replication. Redundancy is maintained over time through…
In modern practical data centers, storage nodes are usually organized into equally sized groups, which is called racks. The cost of cross-rack communication is much more expensive compared with the intra-rack communication cost. The codes…
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…
We focus on two central themes in this dissertation. The first one is on decomposing polytopes and polynomials in ways that allow us to perform nonlinear optimization. We start off by explaining important results on decomposing a polytope…
We consider the problem of {\em restructuring} compressed texts without explicit decompression. We present algorithms which allow conversions from compressed representations of a string $T$ produced by any grammar-based compression…
Polynomial remainder codes are a large class of codes derived from the Chinese remainder theorem that includes Reed-Solomon codes as a special case. In this paper, we revisit these codes and study them more carefully than in previous work.…