Finding Small Fundamental Instantons of LDPC Codes by Path Extension

Junjun GUO; Jianjun MU; Xiaopeng JIAO; Guiping LI

doi:10.1587/transfun.E97.A.1001

Finding Small Fundamental Instantons of LDPC Codes by Path Extension

Junjun GUO, Jianjun MU, Xiaopeng JIAO, Guiping LI

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In this letter, we present a new scheme to find small fundamental instantons (SFIs) of regular low-density parity-check (LDPC) codes for the linear programming (LP) decoding over the binary symmetric channel (BSC). Based on the fact that each instanton-induced graph (IIG) contains at least one short cycle, we determine potential instantons by constructing possible IIGs which contain short cycles and additional paths connected to the cycles. Then we identify actual instantons from potential ones under the LP decoding. Simulation results on some typical LDPC codes show that our scheme is effective, and more instantons can be obtained by the proposed scheme when compared with the existing instanton search method.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E97-A No.4 pp.1001-1004

Publication Date: 2014/04/01

Publicized

Online ISSN: 1745-1337

DOI: 10.1587/transfun.E97.A.1001

Type of Manuscript: LETTER

Category: Coding Theory

Authors

Junjun GUO
  Xidian University
Jianjun MU
  Xidian University
Xiaopeng JIAO
  Xidian University
Guiping LI
  Xidian University

Keyword

instanton, error floor, low-density parity-check (LDPC) codes, linear programming (LP)

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Junjun GUO, Jianjun MU, Xiaopeng JIAO, Guiping LI, "Finding Small Fundamental Instantons of LDPC Codes by Path Extension" in IEICE TRANSACTIONS on Fundamentals, vol. E97-A, no. 4, pp. 1001-1004, April 2014, doi: 10.1587/transfun.E97.A.1001.
Abstract: In this letter, we present a new scheme to find small fundamental instantons (SFIs) of regular low-density parity-check (LDPC) codes for the linear programming (LP) decoding over the binary symmetric channel (BSC). Based on the fact that each instanton-induced graph (IIG) contains at least one short cycle, we determine potential instantons by constructing possible IIGs which contain short cycles and additional paths connected to the cycles. Then we identify actual instantons from potential ones under the LP decoding. Simulation results on some typical LDPC codes show that our scheme is effective, and more instantons can be obtained by the proposed scheme when compared with the existing instanton search method.
URL: https://globals.ieice.org/en_transactions/fundamentals/10.1587/transfun.E97.A.1001/_p

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@ARTICLE{e97-a_4_1001,
author={Junjun GUO, Jianjun MU, Xiaopeng JIAO, Guiping LI, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Finding Small Fundamental Instantons of LDPC Codes by Path Extension},
year={2014},
volume={E97-A},
number={4},
pages={1001-1004},
abstract={In this letter, we present a new scheme to find small fundamental instantons (SFIs) of regular low-density parity-check (LDPC) codes for the linear programming (LP) decoding over the binary symmetric channel (BSC). Based on the fact that each instanton-induced graph (IIG) contains at least one short cycle, we determine potential instantons by constructing possible IIGs which contain short cycles and additional paths connected to the cycles. Then we identify actual instantons from potential ones under the LP decoding. Simulation results on some typical LDPC codes show that our scheme is effective, and more instantons can be obtained by the proposed scheme when compared with the existing instanton search method.},
keywords={},
doi={10.1587/transfun.E97.A.1001},
ISSN={1745-1337},
month={April},}

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TY - JOUR
TI - Finding Small Fundamental Instantons of LDPC Codes by Path Extension
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1001
EP - 1004
AU - Junjun GUO
AU - Jianjun MU
AU - Xiaopeng JIAO
AU - Guiping LI
PY - 2014
DO - 10.1587/transfun.E97.A.1001
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E97-A
IS - 4
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - April 2014
AB - In this letter, we present a new scheme to find small fundamental instantons (SFIs) of regular low-density parity-check (LDPC) codes for the linear programming (LP) decoding over the binary symmetric channel (BSC). Based on the fact that each instanton-induced graph (IIG) contains at least one short cycle, we determine potential instantons by constructing possible IIGs which contain short cycles and additional paths connected to the cycles. Then we identify actual instantons from potential ones under the LP decoding. Simulation results on some typical LDPC codes show that our scheme is effective, and more instantons can be obtained by the proposed scheme when compared with the existing instanton search method.
ER -