Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Coding for Sequence Reconstruction for Single Edits   The sequence reconstruction problem, introduced by Levenshtein in 2001,
considers a communication scenario where the sender transmits a codeword from
some codebook and the receiver obtains multiple noisy reads of the codeword.
The common setup assumes the codebook to be the entire space and the problem is
to determine the minimum number of distinct reads that is required to
reconstruct the transmitted codeword.
  Motivated by modern storage devices, we study a variant of the problem where
the number of noisy reads $N$ is fixed. Specifically, we design reconstruction
codes that reconstruct a codeword from $N$ distinct noisy reads. We focus on
channels that introduce single edit error (i.e. a single substitution,
insertion, or deletion) and their variants, and design reconstruction codes for
all values of $N$. In particular, for the case of a single edit, we show that
as the number of noisy reads increases, the number of redundant bits required
can be gracefully reduced from $\log n+O(1)$ to $\log \log n+O(1)$, and then to
$O(1)$, where $n$ denotes the length of a codeword. We also show that the
redundancy of certain reconstruction codes is within one bit of optimality.

17
The categories of this paper are: q-fin
30
The categories of this paper are: q-alg
26
The categories of this paper are: bayes-an
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
18
The categories of this paper are: econ
34
The categories of this paper are: chem-ph
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org
20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
28
The categories of this paper are: alg-geom
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th