Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Task-based Solutions to Embedded Index Coding   In the index coding problem a sender holds a message $x \in \{0,1\}^n$ and
wishes to broadcast information to $n$ receivers in a way that enables the
$i$th receiver to retrieve the $i$th bit $x_i$. Every receiver has prior side
information comprising a subset of the bits of $x$, and the goal is to minimize
the length of the information sent via the broadcast channel. Porter and
Wootters have recently introduced the model of embedded index coding, where the
receivers also play the role of the sender and the goal is to minimize the
total length of their broadcast information. An embedded index code is said to
be task-based if every receiver retrieves its bit based only on the information
provided by one of the receivers.
  This paper studies the effect of the task-based restriction on linear
embedded index coding. It is shown that for certain side information maps there
exists a linear embedded index code of length quadratically smaller than that
of any task-based embedded index code. The result attains, up to a
multiplicative constant, the largest possible gap between the two quantities.
The proof is by an explicit construction and the analysis involves spectral
techniques.

29
The categories of this paper are: funct-an
7
The categories of this paper are: hep-th
14
The categories of this paper are: math-ph
18
The categories of this paper are: econ
27
The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga
6
The categories of this paper are: astro-ph
16
The categories of this paper are: stat
8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
17
The categories of this paper are: q-fin
36
The categories of this paper are: cmp-lg