Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Parity-Check Density and Achievable Rates of LDPC Codes   The paper introduces new bounds on the asymptotic density of parity-check
matrices and the achievable rates under ML decoding of binary linear block
codes transmitted over memoryless binary-input output-symmetric channels. The
lower bounds on the parity-check density are expressed in terms of the gap
between the channel capacity and the rate of the codes for which reliable
communication is achievable, and are valid for every sequence of binary linear
block codes. The bounds address the question, previously considered by Sason
and Urbanke, of how sparse can parity-check matrices of binary linear block
codes be as a function of the gap to capacity. The new upper bounds on the
achievable rates of binary linear block codes tighten previously reported
bounds by Burshtein et al., and therefore enable to obtain tighter upper bounds
on the thresholds of sequences of binary linear block codes under ML decoding.
The bounds are applied to low-density parity-check (LDPC) codes, and the
improvement in their tightness is exemplified numerically.

16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th
13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn
11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg
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The categories of this paper are: nlin
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The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics
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The categories of this paper are: dg-ga
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The categories of this paper are: bayes-an
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The categories of this paper are: chem-ph