Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Encoding Tasks and R\'enyi Entropy   A task is randomly drawn from a finite set of tasks and is described using a
fixed number of bits. All the tasks that share its description must be
performed. Upper and lower bounds on the minimum $\rho$-th moment of the number
of performed tasks are derived. The case where a sequence of tasks is produced
by a source and $n$ tasks are jointly described using $nR$ bits is considered.
If $R$ is larger than the R\'enyi entropy rate of the source of order
$1/(1+\rho)$ (provided it exists), then the $\rho$-th moment of the ratio of
performed tasks to $n$ can be driven to one as $n$ tends to infinity. If $R$ is
smaller than the R\'enyi entropy rate, this moment tends to infinity. The
results are generalized to account for the presence of side-information. In
this more general setting, the key quantity is a conditional version of R\'enyi
entropy that was introduced by Arimoto. For IID sources two additional
extensions are solved, one of a rate-distortion flavor and the other where
different tasks may have different nonnegative costs. Finally, a divergence
that was identified by Sundaresan as a mismatch penalty in the Massey-Arikan
guessing problem is shown to play a similar role here.

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The categories of this paper are: q-fin
16
The categories of this paper are: stat
26
The categories of this paper are: bayes-an
23
The categories of this paper are: solv-int
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The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
29
The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
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The categories of this paper are: acc-phys
7
The categories of this paper are: hep-th
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-ex
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The categories of this paper are: dg-ga