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pro vyhledávání: '"Yaakobi A"'
The channel output entropy of a transmitted sequence is the entropy of the possible channel outputs and similarly the channel input entropy of a received sequence is the entropy of all possible transmitted sequences. The goal of this work is to study
Externí odkaz:
http://arxiv.org/abs/2407.10026
Robust Gray codes were introduced by (Lolck and Pagh, SODA 2024). Informally, a robust Gray code is a (binary) Gray code $\mathcal{G}$ so that, given a noisy version of the encoding $\mathcal{G}(j)$ of an integer $j$, one can recover $\hat{j}$ that i
Externí odkaz:
http://arxiv.org/abs/2406.17689
This paper presents a novel approach to address the constrained coding challenge of generating almost-balanced sequences. While strictly balanced sequences have been well studied in the past, the problem of designing efficient algorithms with small r
Externí odkaz:
http://arxiv.org/abs/2405.08625
Enzymatic DNA labeling is a powerful tool with applications in biochemistry, molecular biology, biotechnology, medical science, and genomic research. This paper contributes to the evolving field of DNA-based data storage by presenting a formal framew
Externí odkaz:
http://arxiv.org/abs/2405.08475
Motivated by applications in spatial genomics, we revisit group testing (Dorfman~1943) and propose the class of $\lambda$-{\sf ADD}-codes, studying such codes with certain distance $d$ and codelength $n$. When $d$ is constant, we provide explicit cod
Externí odkaz:
http://arxiv.org/abs/2405.06870
We investigate the problem of privately recovering a single erasure for Reed-Solomon codes with low communication bandwidths. For an $[n,k]_{q^\ell}$ code with $n-k\geq q^{m}+t-1$, we construct a repair scheme that allows a client to recover an arbit
Externí odkaz:
http://arxiv.org/abs/2405.06583
Motivated by DNA based data storage system, we investigate the errors that occur when synthesizing DNA strands in parallel, where each strand is appended one nucleotide at a time by the machine according to a template supersequence. If there is a cyc
Externí odkaz:
http://arxiv.org/abs/2405.02080
Composite DNA is a recent method to increase the base alphabet size in DNA-based data storage.This paper models synthesizing and sequencing of composite DNA and introduces coding techniques to correct substitutions, losses of entire strands, and symb
Externí odkaz:
http://arxiv.org/abs/2404.12868
In this work we consider a generalization of the well-studied problem of coding for ``stuck-at'' errors, which we refer to as ``strong stuck-at'' codes. In the traditional framework of stuck-at codes, the task involves encoding a message into a one-d
Externí odkaz:
http://arxiv.org/abs/2403.19061
Autor:
Singhvi, Shubhransh, Gupta, Charchit, Boruchovsky, Avital, Goldberg, Yuval, Kiah, Han Mao, Yaakobi, Eitan
Owing to its immense storage density and durability, DNA has emerged as a promising storage medium. However, due to technological constraints, data can only be written onto many short DNA molecules called data blocks that are stored in an unordered w
Externí odkaz:
http://arxiv.org/abs/2403.15827