Table 3 Optimal node degree distribution of MET-LDPC codes at different code rates
Ref. | Code rate | Degree distribution |
|---|---|---|
[58] | 0.02 | \(\nu ( \boldsymbol{r}, \boldsymbol{x} ) = 0.0225r_{1}x_{1}^{2}x_{2}^{52}+0.0175r_{1}x_{1}^{3}x_{2}^{57}+0.96r_{1}x_{3}^{1} \) |
\(\mu ( \boldsymbol{x} ) = 0.0165x_{1}^{4}+0.0035x_{1}^{9}+0.2475x_{2}^{3}x_{3}^{1}+0.7125x_{2}^{2}x_{3}^{1} \) | ||
[75] | 0.025 | \(\nu ( \boldsymbol{r}, \boldsymbol{x} ) = 0.8711r_{1}x_{1}^{1}+0.0669r_{1}x_{2}^{3}x_{3}^{2}+0.0081r_{1}x_{2}^{4}x_{3}^{2}+0.0015r_{1}x_{2}^{27}x_{3}^{3}+0.0524r_{1}x_{2}^{28}x_{3}^{3} \) |
\(\mu ( \boldsymbol{x} ) = 0.8711x_{1}^{1}x_{2}^{2}+0.1039x_{3}^{3} \) | ||
[76] | 0.03 | \(\nu ( \boldsymbol{r}, \boldsymbol{x} ) = 0.0249r_{1}x_{1}^{2}x_{2}^{50}+0.0219r_{1}x_{1}^{3}x_{2}^{50}+0.9532r_{1}x_{3}^{1} \) |
\(\mu ( \boldsymbol{x} ) = 0.0105x_{1}^{5}+0.0063x_{1}^{10}+0.5196x_{2}^{2}x_{3}^{1}+0.4336x_{2}^{3}x_{3}^{1} \) | ||
[58] | 0.05 | \(\nu ( \boldsymbol{r}, \boldsymbol{x} ) = 0.05625r_{1}x_{1}^{2}x_{2}^{20}+0.04375r_{1}x_{1}^{3}x_{2}^{25}+0.90r_{1}x_{3}^{1} \) |
\(\mu ( \boldsymbol{x} ) = 0.0265625x_{1}^{3}+0.0234375x_{1}^{7}+0.48125x_{2}^{2}x_{3}^{1}+0.41875x_{2}^{3}x_{3}^{1} \) | ||
[76] | 0.06 | \(\nu ( \boldsymbol{r}, \boldsymbol{x} ) = 0.0522r_{1}x_{1}^{2}x_{2}^{37}+0.0291r_{1}x_{1}^{3}x_{2}^{21}+0.9187r_{1}x_{3}^{1} \) |
\(\mu ( \boldsymbol{x} ) = 0.0213x_{1}^{9}+0.2136x_{2}^{2}x_{3}^{1}+0.7051x_{2}^{3}x_{3}^{1} \) | ||
[76] | 0.07 | \(\nu ( \boldsymbol{r}, \boldsymbol{x} ) = 0.0408r_{1}x_{1}^{2}x_{2}^{28}+0.048r_{1}x_{1}^{3}x_{2}^{29}+0.9112r_{1}x_{3}^{1} \) |
\(\mu ( \boldsymbol{x} ) = 0.0188x_{1}^{12}+0.1992x_{2}^{2}x_{3}^{1}+0.712x_{2}^{3}x_{3}^{1} \) | ||
[58] | 0.10 | \(\nu ( \boldsymbol{r}, \boldsymbol{x} ) = 0.075r_{1}x_{1}^{2}x_{2}^{21}+0.05r_{1}x_{1}^{3}x_{2}^{20}+0.875r_{1}x_{3}^{1} \) |
\(\mu ( \boldsymbol{x} ) = 0.025x_{1}^{12}+0.825x_{2}^{3}x_{3}^{1}+0.05x_{2}^{2}x_{3}^{1} \) | ||
[77] | 0.15 | \(\nu ( \boldsymbol{r}, \boldsymbol{x} ) = 0.0858r_{1}x_{1}^{2}x_{2}^{12}+0.0996r_{1}x_{1}^{3}x_{2}^{14}+0.8146r_{1}x_{3}^{1} \) |
\(\mu ( \boldsymbol{x} ) = 0.0160x_{1}^{10}+0.0194x_{1}^{16}+0.0198x_{2}^{2}x_{3}^{1}+0.7948x_{2}^{3}x_{3}^{1} \) | ||
[35] | 0.19 | \(\nu ( \boldsymbol{r}, \boldsymbol{x} ) = 0.1425r_{1}x_{1}^{2}x_{2}^{13}+0.0950r_{1}x_{1}^{3}x_{2}^{7}+0.7625r_{1}{x}_{3}^{1} \) |
\(\mu ( \boldsymbol{x} ) = 0.0475x_{1}^{12}+0.5325x_{2}^{3}x_{3}^{1}+0.2300x_{2}^{4}x_{3}^{1} \) |