Capacity Results for the Noisy Shuffling Channel

Shomorony, Ilan; Heckel, Reinhard

doi:10.1109/isit.2019.8849789

Cited by 55 publications

(40 citation statements)

References 22 publications

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“…. storage," the authors of [17] studied the storage capacity of a model where DNA codewords first experienced the deleterious effects of a DMC (e.g., a binary symmetric channel), and were then fragmented, and subsequently, the fragments were randomly permuted. (Unlike [15], the receiver had access to all the permuted fragments in this model for simplicity.)…”

Section: A Related Literature and Motivationmentioning

confidence: 99%

Coding Theorems for Noisy Permutation Channels

Makur

2020

IEEE Trans. Inform. Theory

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In this paper, we formally define and analyze the class of noisy permutation channels. The noisy permutation channel model constitutes a standard discrete memoryless channel (DMC) followed by an independent random permutation that reorders the output codeword of the DMC. While coding theoretic aspects of this model have been studied extensively, particularly in the context of reliable communication in network settings where packets undergo transpositions, and closely related models of DNA based storage systems have also been analyzed recently, we initiate an information theoretic study of this model by defining an appropriate notion of noisy permutation channel capacity. Specifically, on the achievability front, we prove a lower bound on the noisy permutation channel capacity of any DMC in terms of the rank of the stochastic matrix of the DMC. On the converse front, we establish two upper bounds on the noisy permutation channel capacity of any DMC whose stochastic matrix is strictly positive (entry-wise). Together, these bounds yield coding theorems that characterize the noisy permutation channel capacities of every strictly positive and "full rank" DMC, and our achievability proof yields a conceptually simple, computationally efficient, and capacity achieving coding scheme for such DMCs. Furthermore, we also demonstrate the relation between the wellknown output degradation preorder over channels and noisy permutation channel capacity. In fact, the proof of one of our converse bounds exploits a degradation result that constructs a symmetric channel for any DMC such that the DMC is a degraded version of the symmetric channel. Finally, we illustrate some examples such as the special cases of binary symmetric channels and (general) erasure channels. Somewhat surprisingly, our results suggest that noisy permutation channel capacities are generally quite agnostic to the parameters that define the DMCs.

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Section: A Related Literature and Motivationmentioning

confidence: 99%

Coding Theorems for Noisy Permutation Channels

Makur

2020

IEEE Trans. Inform. Theory

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“…While previous works have proposed several coding schemes, there has been little understanding of the optimal tradeoff between writing cost (bases synthesized/information bit) and reading cost (bases sequenced/information bit). Recent work in [15] and [16] studied the information-theoretic capacity of a DNAbased storage channel, however the work has limited practical applicability due to various unrealistic assumptions and the asymptotic nature of their results.…”

Section: Previous Workmentioning

confidence: 99%

“…In this section, we consider a simplified model for DNAbased storage to develop a better understanding of the coding theoretic tradeoffs. While several previous works such as [15], [16], [18] theoretically analyze various aspects of the DNA-based storage problem (such as the information-theoretic capacity in the asymptotic setting and the optimality of various techniques to recover the order of the oligonucleotides), our main focus is to understand the tradeoff between the writing and reading cost associated with DNA-based storage and to motivate the scheme described in Section 3.…”

Section: Theoretical Analysismentioning

confidence: 99%

Improved read/write cost tradeoff in DNA-based data storage using LDPC codes

Chandak

Tatwawadi

Lau

et al. 2019

Preprint

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With the amount of data being stored increasing rapidly, there is significant interest in exploring alternative storage technologies. In this context, DNA-based storage systems can offer significantly higher storage densities (petabytes/gram) and durability (thousands of years) than current technologies. Specifically, DNA has been found to be stable over extended periods of time which has been demonstrated in the analysis of organisms long since extinct. Recent advances in DNA sequencing and synthesis pipelines have made DNA-based storage a promising candidate for the storage technology of the future.Recently, there have been multiple efforts in this direction, focusing on aspects such as error correction for synthesis/sequencing errors and erasure correction for handling missing sequences. The typical approach is to use separate codes for handling errors and erasures, but there is limited understanding of the efficiency of this framework. Furthermore, the existing techniques use short block-length codes and heavily rely on read consensus, both of which are known to be suboptimal in coding theory.In this work, we study the tradeoff between the writing and reading costs involved in DNA-based storage and propose a practical scheme to achieve an improved tradeoff between these quantities. Our scheme breaks with the traditional separation framework and instead uses a single large block-length LDPC code for both erasure and error correction. We also introduce novel techniques to handle insertion and deletion errors introduced by the synthesis process. For a range of writing costs, the proposed scheme achieves 30-40% lower reading costs than state-of-the-art techniques on experimental data obtained using array synthesis and Illumina sequencing.

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“…However, codewords there consist of multisets of symbols in some alphabet, and errors are comprised of deletions, insertions, substitutions, and erasures of symbols in the multiset. An information-theoretic treatment of related but abstracted models of DNA-based data storage may be found in [32,33]. Very recently, a model for clustering sequencing outputs according to the relevant DNA strand and codes that allow for correct clustering have been studied in [34].…”

Section: Introductionmentioning

confidence: 99%

Coded Trace Reconstruction

Cheraghchi

Ribeiro

Gabrys

et al. 2019

2019 IEEE Information Theory Workshop (ITW)

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Motivated by average-case trace reconstruction and coding for portable DNA-based storage systems, we initiate the study of coded trace reconstruction, the design and analysis of high-rate efficiently encodable codes that can be efficiently decoded with high probability from few reads (also called traces) corrupted by edit errors. Codes used in current portable DNA-based storage systems with nanopore sequencers are largely based on heuristics, and have no provable robustness or performance guarantees even for an error model with i.i.d. deletions and constant deletion probability. Our work is a first step towards the design of efficient codes with provable guarantees for such systems. We consider a constant rate of i.i.d. deletions, and perform an analysis of marker-based code-constructions. This gives rise to codes with redundancy O(n/ log n) (resp. O(n/ log log n)) that can be efficiently reconstructed from exp(O(log 2/3 n)) (resp. exp(O(log log n) 2/3 )) traces, where n is the message length. Then, we give a construction of a code with O(log n) bits of redundancy that can be efficiently reconstructed from poly(n) traces if the deletion probability is small enough. Finally, we show how to combine both approaches, giving rise to an efficient code with O(n/ log n) bits of redundancy which can be reconstructed from poly(log n) traces for a small constant deletion probability.This point of view naturally leads to the problem of coded trace reconstruction: The goal is to design high rate, efficiently encodable codes whose codewords can be efficiently reconstructed with high probability from very few traces with constant deletion probability. Here, "high rate" refers to a rate approaching 1 as the block length increases. We remark that in such a case, the number of traces must grow with the block length of the code. Coded trace reconstruction is also closely related to and motivated by the read process in portable DNA-based data storage systems, which we discuss below.Motivation A practical motivation for coded trace reconstruction comes from portable DNA-based data storage systems using DNA nanopores, first introduced in [13]. In DNA-based storage, a block of user-defined data is first encoded over the nucleotide alphabet {A, C, G, T }, and then transformed into moderately long strands of DNA through a DNA synthesis process. For ease of synthesis, the DNA strands are usually encoded to have balanced GC-content, so that the fraction of {A, T } and {G, C} bases is roughly the same. To recover the block of data, the associated strand of DNA is sequenced with nanopores, resulting in multiple corrupted reads of its encoding. Although the errors encountered during nanopore sequencing include both deletions/insertions as well as substitution errors, careful read preprocessing alignment [13] allows the processed reads to be viewed as traces of the data block's encoding. As a result, recovering the data block in question can be cast in the setting of trace reconstruction. Due to sequencing delay constraints 1 , it is of great ...

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Capacity Results for the Noisy Shuffling Channel

Cited by 55 publications

References 22 publications

Coding Theorems for Noisy Permutation Channels

Coding Theorems for Noisy Permutation Channels

Improved read/write cost tradeoff in DNA-based data storage using LDPC codes

Coded Trace Reconstruction

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