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Improved linear programming decoding of LDPC codes and bounds on the minimum and fractional distance

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David Burshtein, Idan Goldenberg

Information Theory · Submitted 7 Dec 2010

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim Four contributions to the LP framework are presented.

how it is stated · asserted 1.00 read the record →

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arXiv ID1012.1425 (version 1)
Pith IDQFVGYQRD, Pith's permanent record of this paper and its review
CitationDavid Burshtein, Idan Goldenberg. "Improved linear programming decoding of LDPC codes and bounds on the minimum and fractional distance." arXiv:1012.1425 (2010). https://pith.science/paper/QFVGYQRD
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The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 5,354 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.08 · states limitation 0.16 · human participants 0.01 · controlled comparison 0.08 · randomized assignment 0.01 · states quantitative result 0.55 · compares with prior results 0.87 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

We examine LDPC codes decoded using linear programming (LP). Four contributions to the LP framework are presented. First, a new method of tightening the LP relaxation, and thus improving the LP decoder, is proposed. Second, we present an algorithm which calculates a lower bound on the minimum distance of a specific code. This algorithm exhibits complexity which scales quadratically with the block length. Third, we propose a method to obtain a tight lower bound on the fractional distance, also with quadratic complexity, and thus less than previously-existing methods. Finally, we show how the fundamental LP polytope for generalized LDPC codes and nonbinary LDPC codes can be obtained.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We examine LDPC codes decoded using linear programming (LP). background 0.92 0.61 0.04 asserted 0.85
s1 Four contributions to the LP framework are presented. contribution 1.00 0.90 0.08 asserted 1.00
s2 First, a new method of tightening the LP relaxation, and thus improving the LP decoder, is proposed. contribution 1.00 0.93 0.21 asserted 0.96
s3 Second, we present an algorithm which calculates a lower bound on the minimum distance of a specific code. contribution 0.99 0.93 0.08 asserted 1.00
s4 This algorithm exhibits complexity which scales quadratically with the block length. result 0.80 0.88 0.04 asserted 1.00
s5 Third, we propose a method to obtain a tight lower bound on the fractional distance, also with quadratic complexity, and thus less than previously-existing methods. contribution 0.99 0.94 0.15 asserted 0.99
s6 Finally, we show how the fundamental LP polytope for generalized LDPC codes and nonbinary LDPC codes can be obtained. contribution 1.00 0.93 0.12 asserted 1.00

What kind of paper the classifier reports this is: method or tool 1.00 · evidence from proof or derivation 0.94.

What was examined, and what was not

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  • figures and tables
  • references and citing sentences
  • relations to other papers
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  • P abstract
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  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

We examine LDPC codes decoded using linear programming (LP). Four contributions to the LP framework are presented. First, a new method of tightening the LP relaxation, and thus improving the LP decoder, is proposed. Second, we present an algorithm which calculates a lower bound on the minimum distance of a specific code. This algorithm exhibits complexity which scales quadratically with the block length. Third, we propose a method to obtain a tight lower bound on the fractional distance, also with quadratic complexity, and thus less than previously-existing methods. Finally, we show how the fundamental LP polytope for generalized LDPC codes and nonbinary LDPC codes can be obtained.

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How the literature uses it

1 arXiv paper cite this in 4 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 3 sentences without a confident label

Uses its method or tool 1 paper
  • To do this, we use the procedure described in [ref] which obtains a lower bound $LB(_1)$ on the minimum distance of the randomly-drawn code $_1$.

    The approximate maximum-likelihood certificate · Application of the AMLC to expurgated LDPC ensembles · 1.00

What it cites · 4 sentences without a confident label

Cites as background 1 paper

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