On the Minimum-Weight Codewords of Array LDPC Codes with Column Weight 4

Haiyang LIU; Gang DENG; Jie CHEN

doi:10.1587/transfun.E97.A.2236

On the Minimum-Weight Codewords of Array LDPC Codes with Column Weight 4

Haiyang LIU, Gang DENG, Jie CHEN

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In this paper, we investigate the minimum-weight codewords of array LDPC codes C(m,q), where q is an odd prime and m ≤ q. Using some analytical approaches, the lower bound on the number of minimum-weight codewords of C(m,q) given by Kaji (IEEE Int. Symp. Inf. Theory, June/July 2009) is proven to be tight for m = 4 and q > 19. In other words, C(4,q) has 4q²(q-1) minimum-weight codewords for all q > 19. In addition, we show some interesting universal properties of the supports of generators of minimum-weight codewords of the code C(4,q)(q > 19).

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E97-A No.11 pp.2236-2246

Publication Date: 2014/11/01

Publicized

Online ISSN: 1745-1337

DOI: 10.1587/transfun.E97.A.2236

Type of Manuscript: PAPER

Category: Coding Theory

Authors

Haiyang LIU
  Chinese Academy of Sciences
Gang DENG
  Chinese Academy of Sciences
Jie CHEN
  Chinese Academy of Sciences

Keyword

low-density parity-check (LDPC) code, array code, minimum-weight codeword, cyclic shift closure

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Haiyang LIU, Gang DENG, Jie CHEN, "On the Minimum-Weight Codewords of Array LDPC Codes with Column Weight 4" in IEICE TRANSACTIONS on Fundamentals, vol. E97-A, no. 11, pp. 2236-2246, November 2014, doi: 10.1587/transfun.E97.A.2236.
Abstract: In this paper, we investigate the minimum-weight codewords of array LDPC codes C(m,q), where q is an odd prime and m ≤ q. Using some analytical approaches, the lower bound on the number of minimum-weight codewords of C(m,q) given by Kaji (IEEE Int. Symp. Inf. Theory, June/July 2009) is proven to be tight for m = 4 and q > 19. In other words, C(4,q) has 4q²(q-1) minimum-weight codewords for all q > 19. In addition, we show some interesting universal properties of the supports of generators of minimum-weight codewords of the code C(4,q)(q > 19).
URL: https://globals.ieice.org/en_transactions/fundamentals/10.1587/transfun.E97.A.2236/_p

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@ARTICLE{e97-a_11_2236,
author={Haiyang LIU, Gang DENG, Jie CHEN, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={On the Minimum-Weight Codewords of Array LDPC Codes with Column Weight 4},
year={2014},
volume={E97-A},
number={11},
pages={2236-2246},
abstract={In this paper, we investigate the minimum-weight codewords of array LDPC codes C(m,q), where q is an odd prime and m ≤ q. Using some analytical approaches, the lower bound on the number of minimum-weight codewords of C(m,q) given by Kaji (IEEE Int. Symp. Inf. Theory, June/July 2009) is proven to be tight for m = 4 and q > 19. In other words, C(4,q) has 4q²(q-1) minimum-weight codewords for all q > 19. In addition, we show some interesting universal properties of the supports of generators of minimum-weight codewords of the code C(4,q)(q > 19).},
keywords={},
doi={10.1587/transfun.E97.A.2236},
ISSN={1745-1337},
month={November},}

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TY - JOUR
TI - On the Minimum-Weight Codewords of Array LDPC Codes with Column Weight 4
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 2236
EP - 2246
AU - Haiyang LIU
AU - Gang DENG
AU - Jie CHEN
PY - 2014
DO - 10.1587/transfun.E97.A.2236
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E97-A
IS - 11
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - November 2014
AB - In this paper, we investigate the minimum-weight codewords of array LDPC codes C(m,q), where q is an odd prime and m ≤ q. Using some analytical approaches, the lower bound on the number of minimum-weight codewords of C(m,q) given by Kaji (IEEE Int. Symp. Inf. Theory, June/July 2009) is proven to be tight for m = 4 and q > 19. In other words, C(4,q) has 4q²(q-1) minimum-weight codewords for all q > 19. In addition, we show some interesting universal properties of the supports of generators of minimum-weight codewords of the code C(4,q)(q > 19).
ER -