Find below a list of low-density parity-check (LDPC) codes (generating polynomials and thresholds) and matrices (in the alist format proposed by D. MacKay, M. Davey, and J. Lafferty) particularly optimized for different coding rates and communication channels.
Codes were computed using the discretized density evolution algorithm.
Matrices for different block lengths were constructed using the original progressive edge-growth (PEG) algorithm.
Rate | Generating Polynomials | Threshold | Matrices |
---|---|---|---|
0.5 | λ(x) = 0.23802 x + 0.20997 x^{2} + 0.03492 x^{3} + 0.12015 x^{4} + 0.01587 x^{6} + 0.00480 x^{13} + 0.37627 x^{14} | 0.1493 | N=10^{4} |
ρ(x) = 0.98013 x^{7} + 0.01987 x^{8} | |||
0.6 | λ(x) = 0.160608 x + 0.134533 x^{2} + 0.0482729 x^{3} + 0.0468901 x^{4} + 0.102275 x^{7} + 0.102575 x^{8} + 0.0454141 x^{10} + 0.359432 x^{44} | 0.829355 | N=10^{4} |
ρ(x) = 0.314523 x^{12} + 0.685477 x^{13} | |||
Rate | Generating Polynomials | Threshold | Matrices |
---|---|---|---|
0.3 | λ(x) = 0.247205 x + 0.225225 x^{2} + 0.0543745 x^{3} + 0.153518 x^{8} + 0.168646 x^{9} + 0.151032 x^{39} | 0.180247 | N=10^{4} |
ρ(x) = 0.24935 x^{4} + 0.75065 x^{5} | |||
0.4 | λ(x) = 0.181749 x + 0.147329 x^{2} + 0.0544272 x^{3} + 0.0707276 x^{4} + 0.0686918 x^{6} + 0.135139 x^{8} + 0.159581 x^{34} + 0.182355 x^{39} | 0.140508 | N=10^{4} |
ρ(x) = 0.712734 x^{7} + 0.287266 x^{8} | |||
0.5 | λ(x) = 0.159673 x + 0.121875 x^{2} + 0.11261 x^{3} + 0.190871 x^{4} + 0.0770616 x^{9} + 0.337909 x^{24} | 0.102592 |
N=2×10^{3} N=10^{4} N=10^{5} N=2×10^{5} |
ρ(x) = 0.360479 x^{8} + 0.639521 x^{9} | |||
0.6 | λ(x) = 0.11653 x + 0.125646 x^{2} + 0.108507 x^{3} + 0.0534223 x^{4} + 0.0727228 x^{6} + 0.0347964 x^{7} + 0.0729986 x^{8} + 0.0752607 x^{17} + 0.117103 x^{31} + 0.223013 x^{44} | 0.0745261 |
N=10^{4} N=10^{5} N=2×10^{5} |
ρ(x) = 0.582731 x^{13} + 0.417269 x^{14} | |||
0.7 | λ(x) = 0.091699 x + 0.171401 x^{2} + 0.0683878 x^{3} + 0.120523 x^{4} + 0.187471 x^{10} + 0.208278 x^{27} + 0.152239 x^{29} | 0.0501875 |
N=10^{4} N=10^{5} N=2×10^{5} |
ρ(x) = 0.806453 x^{18} + 0.193547 x^{19} | |||
0.8 | λ(x) = 0.0667948 x 0.194832 x^{2} + 0.0570523 x^{3} + 0.0645024 x^{4} + 0.204606 x^{8} + 0.0964409 x^{14} + 0.23872 x^{28} + 0.0770523 x^{34} | 0.0289413 |
N=2×10^{3} N=10^{4} N=10^{5} N=2×10^{5} |
ρ(x) = 0.708874 x^{29} + 0.291126 x^{30} | |||