Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Optimal Reconstruction Codes for Deletion Channels   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.
Motivated by modern storage devices, we introduced a variant of the problem
where the number of noisy reads $N$ is fixed (Kiah et al. 2020). Of
significance, for the single-deletion channel, using $\log_2\log_2 n +O(1)$
redundant bits, we designed a reconstruction code of length $n$ that
reconstructs codewords from two distinct noisy reads.
  In this work, we show that $\log_2\log_2 n -O(1)$ redundant bits are
necessary for such reconstruction codes, thereby, demonstrating the optimality
of our previous construction. Furthermore, we show that these reconstruction
codes can be used in $t$-deletion channels (with $t\ge 2$) to uniquely
reconstruct codewords from $n^{t-1}+O\left(n^{t-2}\right)$ distinct noisy
reads.

21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
19
The categories of this paper are: eess
36
The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an
23
The categories of this paper are: solv-int
16
The categories of this paper are: stat
5
The categories of this paper are: gr-qc
37
The categories of this paper are: supr-con
11
The categories of this paper are: hep-lat