Adversarial Torn-paper Codes

Bar-Lev, Daniella; Marcovich, Sagi; Yaakobi, Eitan; Yehezkeally, Yonatan

doi:10.48550/arxiv.2201.11150

Cited by 1 publication

(2 citation statements)

References 29 publications

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“…Now, a careful concatenation of the index, the RLL encoded string and the header (described in Algorithm 1 in [31] and Figure 9), leads to a codebook which is a (L min , L max )-single strand torn-paper code, which achieves a zero-error rate of 1 − 1/a. Moreover, [57] shows that this achievable rate is the zero-error capacity of the adversarial TPC.…”

Section: Index-based Coding Via Unique Headers For the Torn-paper Cha...mentioning

confidence: 88%

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An Information Theory for Out-of-Order Media With Applications in DNA Data Storage

Ravi,

Vahid,

Shomorony

2024

IEEE Trans. Mol. Biol. Multi-Scale Commun.

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Recent advancements in DNA-based storage prototypes focus on encoding information across multiple DNA molecules. This approach utilizes high-throughput sequencing technologies, leading to outputs that are out-of-order. We study the shuffling channel, where input codewords are split into fixed-size fragments. We show that achieving channel capacity uses index-based coding, which assigns unique indices to each fragment. We also introduce two more complex channels, which aim to model popular sequencing strategies in DNA sequencing. In the torn-paper channel, the input codeword is torn up into fragments of random sizes, while in the shotgun sequencing channel, fixed-length random substrings of the input codeword are observed at the output. In both of these channels, the lack of ordering cannot be circumvented by simply adding unique indices to the fragments. We show how the capacity of both of these channels can be achieved using random codes. We introduce and analyze code constructions based on index sequences. While these codes are computationally efficient, they are not capacityachieving, and we leave the questions of finding efficient capacityachieving codes for these settings as open problems.

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Section: Index-based Coding Via Unique Headers For the Torn-paper Cha...mentioning

confidence: 88%

“…+ for the capacity C ZE,aTPC = (1 − 1/a) + established in [57]. We note that C ZE,aTPC = 0 when L min < log n. Therefore we focus on the regime where L min ≥ log n.…”

Section: !(#)mentioning

confidence: 99%