Research AreasPublications

The sequence reconstruction problem, introduced by Levenshtein in 2001, considers a scenario where the sender transmits a codeword from some codebook, and the receiver obtains N noisy outputs of the codeword. We study the problem of efficient reconstruction using N outputs that are corrupted by substitutions. Specifically, for the ubiquitous Reed-Solomon codes, we adapt the Koetter-Vardy soft-decoding algorithm, pre- senting a reconstruction algorithm capable of correcting beyond Johnson radius. Furthermore, the algorithm uses O(n N) field operations, where n is the codeword length.

DNA emerges as a promising medium for the exponential growth of digital data due to its density and durability. This study extends recent research by addressing the coverage depth problem in practical scenarios, exploring optimal error-correcting code pairings with DNA storage systems to minimize coverage depth. Conducted within random access settings, the study provides theoretical analyses and experimental simulations to examine the expectation and probability distribution of samples needed for files recovery. Structured into sections covering definitions, analyses, lower bounds, and comparative evaluations of coding schemes, the paper unveils insights into effective coding schemes for optimizing DNA storage systems.

Labeling of DNA molecules is a fundamental technique for DNA visualization and analysis. This process was mathematically modeled in [1], where the received sequence indicates the positions of the used labels. In this work, we develop error correcting codes for labeled DNA sequences, establishing bounds and constructing explicit systematic encoders for single substitution, insertion, and deletion errors. We focus on two cases: (1) using the complete set of length-two labels and (2) using the minimal set of length-two labels that ensures the recovery of DNA sequences from their labeling for ‘almost’ all DNA sequences.

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-dimensional binary vector. However, a certain number of the bits in this vector are `frozen’, meaning they are fixed at a predetermined value and cannot be altered by the encoder. The decoder, aware of the proportion of frozen bits but not their specific positions, is responsible for deciphering the intended message. We consider a more challenging version of this problem where the decoder does not even know the fraction of frozen bits. We construct explicit and efficient encoding and decoding algorithms that get arbitrarily close to capacity in this scenario. Furthermore, to the best of our knowledge, our construction is the first fully explicit construction of stuck-at codes that approaches capacity.

Motivation Recent years have seen a growing number and an expanding scope of studies using synthetic oligo libraries for a range of applications in synthetic biology. As experiments are growing by numbers and complexity, analysis tools can facilitate quality control and support better assessment and inference. Results We present a novel analysis tool, called SOLQC, which enables fast and comprehensive analysis of synthetic oligo libraries, based on NGS analysis performed by the user. SOLQC provides statistical information such as the distribution of variant representation, different error rates and their dependence on sequence or library properties. SOLQC produces graphical reports from the analysis, in a flexible format. We demonstrate SOLQC by analyzing literature libraries. We also discuss the potential benefits and relevance of the different components of the analysis.