article · IEEE Transactions on Information Theory · 2021

Systematic Convolutional Low Density Generator Matrix Code

Suihua Cai, Wenchao Lin, Xinyuanmeng Yao, Baodian Wei, Xiao Ma

Cited by 15Abstract and details only

Abstract

In this paper, we propose a systematic low density generator matrix (LDGM) code ensemble, which is defined by the Bernoulli process. We prove that, under maximum likelihood (ML) decoding, the proposed ensemble can achieve the capacity of binary-input output symmetric (BIOS) memoryless channels in terms of bit error rate (BER). The proof technique reveals a new mechanism, different from lowering down frame error rate (FER), that the BER can be lowered down by assigning light codeword vectors to light information vectors. The finite length performance is analyzed by deriving an upper bound and a lower bound, both of which are shown to be tight in the high signal-to-noise ratio (SNR) region. To improve the waterfall performance, we construct the systematic convolutional LDGM (SysConv-LDGM) codes by a random splitting process. The SysConv-LDGM codes are easily configurable in the sense that any rational code rate can be realized without complex optimization. As a universal construction, the main advantage of the SysConv-LDGM codes is their near-capacity performance in the waterfall region and predictable performance in the error-floor region that can be lowered down to any target as required by increasing the density of the uncoupled LDGM codes. Numerical results are also provided to verify our analysis.

Cite this paper

APA 7

Cai, S., Lin, W., Yao, X., Wei, B., & Ma, X. (2021). Systematic Convolutional Low Density Generator Matrix Code. IEEE Transactions on Information Theory, 67(6), 3752–3764. https://doi.org/10.1109/tit.2021.3064922

MLA 9

Cai, Suihua, et al. “Systematic Convolutional Low Density Generator Matrix Code.” IEEE Transactions on Information Theory, vol. 67, no. 6, 2021, pp. 3752–64, https://doi.org/10.1109/tit.2021.3064922.

Chicago

Cai, Suihua, Wenchao Lin, Xinyuanmeng Yao, Baodian Wei, and Xiao Ma. 2021. “Systematic Convolutional Low Density Generator Matrix Code.” IEEE Transactions on Information Theory 67 (6): 3752–64. https://doi.org/10.1109/tit.2021.3064922.

Harvard

Cai, S. et al. (2021) ‘Systematic Convolutional Low Density Generator Matrix Code’, IEEE Transactions on Information Theory, 67(6), pp. 3752–3764. Available at: https://doi.org/10.1109/tit.2021.3064922.

BibTeX

@article{cai2021systematic,
  title = {{Systematic Convolutional Low Density Generator Matrix Code}},
  author = {Cai, Suihua and Lin, Wenchao and Yao, Xinyuanmeng and Wei, Baodian and Ma, Xiao},
  journal = {IEEE Transactions on Information Theory},
  volume = {67},
  number = {6},
  pages = {3752--3764},
  year = {2021},
  doi = {10.1109/tit.2021.3064922}
}

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