Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Channel Coding and Lossy Source Coding Using a Constrained Random Number
  Generator   Stochastic encoders for channel coding and lossy source coding are introduced
with a rate close to the fundamental limits, where the only restriction is that
the channel input alphabet and the reproduction alphabet of the lossy source
code are finite. Random numbers, which satisfy a condition specified by a
function and its value, are used to construct stochastic encoders. The proof of
the theorems is based on the hash property of an ensemble of functions, where
the results are extended to general channels/sources and alternative formulas
are introduced for channel capacity and the rate-distortion region. Since an
ensemble of sparse matrices has a hash property, we can construct a code by
using sparse matrices, where the sum-product algorithm can be used for encoding
and decoding by assuming that channels/sources are memoryless.

11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess
32
The categories of this paper are: atom-ph
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
25
The categories of this paper are: patt-sol
23
The categories of this paper are: solv-int
36
The categories of this paper are: cmp-lg