Related papers: Trellis BMA: Coded Trace Reconstruction on IDS Cha…
Sparse intersymbol-interference (ISI) channels are encountered in a variety of high-data-rate communication systems. Such channels have a large channel memory length, but only a small number of significant channel coefficients. In this…
In the trace reconstruction problem, one seeks to reconstruct a binary string $s$ from a collection of traces, each of which is obtained by passing $s$ through a deletion channel. It is known that $\exp(\tilde O(n^{1/5}))$ traces suffice to…
To make DNA a suitable medium for archival data storage, it is essential to consider the decay process of the strands observed in DNA storage systems. This paper studies the decay process as a probabilistic noisy torn paper channel (TPC),…
The trace reconstruction problem studies the number of noisy samples needed to recover an unknown string $\boldsymbol{x}\in\{0,1\}^n$ with high probability, where the samples are independently obtained by passing $\boldsymbol{x}$ through a…
In the trace reconstruction problem, one observes the output of passing a binary string $s \in \{0,1\}^n$ through a deletion channel $T$ times and wishes to recover $s$ from the resulting $T$ "traces." Most of the literature has focused on…
The coded trace reconstruction problem asks to construct a code $C\subset \{0,1\}^n$ such that any $x\in C$ is recoverable from independent outputs ("traces") of $x$ from a binary deletion channel (BDC). We present binary codes of rate…
Because of its high data density and longevity, DNA is emerging as a promising candidate for satisfying increasing data storage needs. Compared to conventional storage media, however, data stored in DNA is subject to a wider range of errors…
DNA is emerging as an increasingly attractive medium for data storage due to a number of important and unique advantages it offers, most notably the unprecedented durability and density. While the technology is evolving rapidly, the…
This paper introduces a new family of reconstruction codes which is motivated by applications in DNA data storage and sequencing. In such applications, DNA strands are sequenced by reading some subset of their substrings. While previous…
The insertion-deletion channel takes as input a bit string ${\bf x}\in\{0,1\}^{n}$, and outputs a string where bits have been deleted and inserted independently at random. The trace reconstruction problem is to recover $\bf x$ from many…
DNA data storage offers a high-density, long-term alternative to traditional storage systems, addressing the exponential growth of digital data. Composite DNA extends this paradigm by leveraging mixtures of nucleotides to increase storage…
We study the problem of learning a node-labeled tree given independent traces from an appropriately defined deletion channel. This problem, tree trace reconstruction, generalizes string trace reconstruction, which corresponds to the tree…
The prevalent technique for DNA sequencing consists of two main steps: shotgun sequencing, where many randomly located fragments, called reads, are extracted from the overall sequence, followed by an assembly algorithm that aims to…
DNA-based data storage has been attracting significant attention due to its extremely high data storage density, low power consumption, and long duration compared to conventional data storage media. Despite the recent advancements in DNA…
Communications in dispersive direct-sequence code-division multiple-access (DS-CDMA) channels suffer from intersymbol and multiple-access interference, which can significantly impair performance. Joint maximum \textit{a posteriori}…
DNA is an attractive medium for digital data storage. When data is stored on DNA, errors occur, which makes error-correcting coding techniques critical for reliable DNA data storage. To reduce the errors, a common technique is to include…
We describe a strategy for constructing codes for DNA-based information storage by serial composition of weighted finite-state transducers. The resulting state machines can integrate correction of substitution errors; synchronization by…
Motivated by the sequence reconstruction problem from traces in DNA-based storage, we consider the problem of designing codes for the deletion channel when multiple observations (or traces) are available to the decoder. We propose simple…
Owing to its longevity and enormous information density, DNA, the molecule encoding biological information, has emerged as a promising archival storage medium. However, due to technological constraints, data can only be written onto many…
Trace reconstruction is the problem of learning an unknown string $x$ from independent traces of $x$, where traces are generated by independently deleting each bit of $x$ with some deletion probability $q$. In this paper, we initiate the…