Related papers: Constrained Error-Correcting Codes for Efficient D…
Motivated by average-case trace reconstruction and coding for portable DNA-based storage systems, we initiate the study of \emph{coded trace reconstruction}, the design and analysis of high-rate efficiently encodable codes that can be…
The exponential increase in storage demand and low lifespan of data storage devices has resulted in long-term archival and preservation emerging as a critical bottlenecks in data storage. In order to meet this demand, researchers are now…
We study the amount of reliable information that can be stored in a DNA-based storage system composed of short DNA molecules. In this regime, Shomorony and Heckel (2022) put forward a conjecture on the scaling of the number of information…
We study data structures in the presence of adversarial noise. We want to encode a given object in a succinct data structure that enables us to efficiently answer specific queries about the object, even if the data structure has been…
Identifying palindromes in sequences has been an interesting line of research in combinatorics on words and also in computational biology, after the discovery of the relation of palindromes in the DNA sequence with the HIV virus. Efficient…
In this paper, we study the Random Access Problem in DNA storage, which addresses the challenge of retrieving a specific information strand from a DNA-based storage system. In this framework, the data is represented by $k$ information…
Efficient and accurate decoding of quantum error-correcting codes is essential for fault-tolerant quantum computation, however, it is challenging due to the degeneracy of errors, the complex code topology, and the large space for logical…
In modern age, the increasing complexity of computation and communication technology is leading us towards the necessity of new paradigm. As a result, unconventional approach like DNA coding theory is gaining considerable attention. The…
Large language models (LLMs) have achieved notable success in code generation. However, they still frequently produce uncompilable output because their next-token inference procedure does not model formal aspects of code. Although…
We study permutations over the set of $\ell$-grams, that are feasible in the sense that there is a sequence whose $\ell$-gram frequency has the same ranking as the permutation. Codes, which are sets of feasible permutations, protect…
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…
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…
Large language models (LLMs) have shown impressive promise in code generation, yet their progress remains limited by the shortage of large-scale datasets that are both diverse and well-aligned with human reasoning. Most existing resources…
The code that combines channel estimation and error protection has received general attention recently, and has been considered a promising methodology to compensate multi-path fading effect. It has been shown by simulations that such code…
Motivated by applications in DNA-based storage, we study explicit encoding and decoding schemes of binary strings satisfying locally balanced constraints, where the $(\ell,\delta)$-locally balanced constraint requires that the weight of any…
Due to its longevity and enormous information density, DNA is an attractive medium for archival storage. In this work, we study the fundamental limits and tradeoffs of DNA-based storage systems under a simple model, motivated by current…
To ensure that text generated by large language models (LLMs) is in an expected format, constrained decoding proposes to enforce strict formal language constraints during generation. However, as we show in this work, not only do such…
In this paper, we consider a generalized longest common subsequence problem with multiple substring exclusion constrains. For the two input sequences $X$ and $Y$ of lengths $n$ and $m$, and a set of $d$ constrains $P=\{P_1,...,P_d\}$ of…
Quantum error correction is an important building block for reliable quantum information processing. A challenging hurdle in the theory of quantum error correction is that it is significantly more difficult to design error-correcting codes…
We introduce a novel framework for implementing error-correction in constrained systems. The main idea of our scheme, called Quantized-Constraint Concatenation (QCC), is to employ a process of embedding the codewords of an error-correcting…