Error-Correcting Codes for Noisy Duplication Channels

Tang, Yuanyuan; Farnoud, Farzad

doi:10.1109/tit.2021.3059095

Cited by 15 publications

(8 citation statements)

References 21 publications

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“…Several other papers have studied variations of the DNA storage channel model [14], [41], and various papers have proposed and analyzed coding schemes [7], [14], [17], [19], [21], [25], [37], [40], [43], [46], [48]. We refer the reader to [42, Sec.…”

Section: Other Related Workmentioning

confidence: 99%

The DNA Storage Channel: Capacity and Error Probability

Weinberger¹,

Merhav²

2021

Preprint

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The DNA storage channel is considered, in which M Deoxyribonucleic acid (DNA) molecules comprising each codeword, are stored without order, then sampled N times with replacement, and the sequenced over a discrete memoryless channel. For a constant coverage depth M/N and molecule length scaling Θ(log M ), lower (achievability) and upper (converse) bounds on the capacity of the channel, as well as a lower (achievability) bound on the reliability function of the channel are provided. Both the lower and upper bounds on the capacity generalize a bound which was previously known to hold only for the binary symmetric sequencing channel, and only under certain restrictions on the molecule length scaling and the crossover probability parameters. When

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Section: Other Related Workmentioning

confidence: 99%

The DNA Storage Channel: Capacity and Error Probability

Weinberger¹,

Merhav²

2021

Preprint

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“…Fix some string-duplication system S = S(Σ, s, T ). Depending on the application, one can view S in two ways: either as a generative model which describes what possible strings may be derived from s (e.g., see [2], [6], [9], [12], [15], [25]), or as a channel which describes what corrupted versions of the transmitted s may be received (e.g., see [16]- [18], [20], [32], [34], [38]- [40]). While the latter view calls for the construction of suitably tailored error-correcting codes, the former inspires the following properties of S to be studied.…”

Section: Preliminariesmentioning

confidence: 99%

“…Other codes that correct a prescribed number of duplications were constructed in [17], [18], [20], [40], addressing several duplication types. Additional codes that are capable of correcting a mixture of tandem duplications and substitutions or edits were described in [32]- [34]. Finally, some Levenshtein-reconstruction problems for duplications were studied in [38], [39].…”

Section: Introductionmentioning

confidence: 99%

On the Reverse-Complement String-Duplication System

Ben-Tolila¹,

Schwartz²

2021

Preprint

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Motivated by DNA storage in living organisms, and by known biological mutation processes, we study the reverse-complement string-duplication system. We fully classify the conditions under which the system has full expressiveness, for all alphabets and all fixed duplication lengths. We then focus on binary systems with duplication length 2 and prove that they have full capacity, yet surprisingly, have zero entropy-rate. Finally, by using binary single burst-insertion correcting codes, we construct codes that correct a single reverse-complement duplication of odd length, over any alphabet. The redundancy (in bits) of the constructed code does not depend on the alphabet size.

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“…In the future, we believe that a study of reconstruction schemes, with or without list-decoding, is of interest with other error models which affect in-vivo DNA data storage; related models to uniform tandem-duplication noise, which have recently been studied on their own and may now be easier to analyze in that setting, and therefore are a logical first step in this direction, may be bounded tandem-duplication (see, e.g., [10], [11], [15]) or combined uniform-tandem-duplication and substitution noise [25], [26].…”

Section: Related Work and Main Contributionmentioning

confidence: 99%

“…The effects of duplication errors, specifically, were studied in a number of recent works including [10], [11], [14]- [18], [21], [23], [25], [26] among others. These works provided some implicit and explicit constructions for uniform-tandemduplication codes, as well as some bounds.…”

Section: Introductionmentioning

confidence: 99%

Uncertainty of Reconstruction with List-Decoding from Uniform-Tandem-Duplication Noise

Yehezkeally,

Schwartz

2020

Preprint

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We propose a list-decoding scheme for reconstruction codes in the context of uniform-tandem-duplication noise, which can be viewed as an application of the associative memory model to this setting. We find the uncertainty associated with m > 2 strings (where a previous paper considered m = 2) in asymptotic terms, where code-words are taken from an errorcorrecting code. Thus, we find the trade-off between the design minimum distance, the number of errors, the acceptable list size and the resulting uncertainty, which corresponds to the required number of distinct retrieved outputs for successful reconstruction. It is therefore seen that by accepting list-decoding one may decrease coding redundancy, or the required number of reads, or both.

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Error-Correcting Codes for Noisy Duplication Channels

Cited by 15 publications

References 21 publications

The DNA Storage Channel: Capacity and Error Probability

The DNA Storage Channel: Capacity and Error Probability

On the Reverse-Complement String-Duplication System

Uncertainty of Reconstruction with List-Decoding from Uniform-Tandem-Duplication Noise

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