DeepAI AI Chat
Log In Sign Up

Coded trace reconstruction

by   Mahdi Cheraghchi, et al.
University of Illinois at Urbana-Champaign
Imperial College London

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/ n) (resp. O(n/ n)) that can be efficiently reconstructed from (O(^2/3n)) (resp. (O( n)^2/3)) traces, where n is the message length. Then, we give a construction of a code with O( 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/ n) bits of redundancy which can be reconstructed from poly( n) traces for a small constant deletion probability.


page 1

page 2

page 3

page 4


Coded trace reconstruction in a constant number of traces

The coded trace reconstruction problem asks to construct a code C⊂{0,1}^...

Coding for Trace Reconstruction over Multiple Channels with Vanishing Deletion Probabilities

Motivated by DNA-based storage applications, we study the problem of rec...

Trellis BMA: Coded Trace Reconstruction on IDS Channels for DNA Storage

Sequencing a DNA strand, as part of the read process in DNA storage, pro...

Optimal Codes Detecting Deletions in Concatenated Binary Strings Applied to Trace Reconstruction

Consider two or more strings 𝐱^1,𝐱^2,…, that are concatenated to form 𝐱=...

Coding for Deletion Channels with Multiple Traces

Motivated by the sequence reconstruction problem from traces in DNA-base...

Coding for Sequence Reconstruction for Single Edits

The sequence reconstruction problem, introduced by Levenshtein in 2001, ...

Trace Reconstruction Problems in Computational Biology

The problem of reconstructing a string from its error-prone copies, the ...