Role of the Product λ′(0)ρ′(1) in Determining LDPC Code Performance
Abstract
:1. Introduction
2. Graphical Representation of LDPC Codes
3. Gaussian Approximation
4. Mathematical Method of [16]
5. Upper Bounds on LDPC Codes Decoding Thresholds
5.1. Upper Bound on LDPC Codes Decoding Thresholds Holding for
5.2. Further Upper Bounds on LDPC Codes Decoding Thresholds Holding for
6. Role of the Product in Determining the Weight Distribution of LDPC Codes
7. Role of the Product in Determining the Decoding Threshold of LDPC Codes
8. Numeric Results
9. Discussion and Simulation Results
- and
- .
9.1. Case 1:
9.2. Case 2:
10. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Appendix A. Approximation of the Functions and
- s[y_] = Interpolation[v, y];
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4 | 6 | 7 | 8 | |
---|---|---|---|---|
0.38354 | 0.33241 | 0.31570 | 0.30013 | |
0.04237 | 0.24632 | 0.41672 | 0.28395 | |
0.57409 | 0.11014 | |||
0.31112 | ||||
0.43810 | ||||
0.41592 | ||||
0.24123 | ||||
0.75877 | 0.76611 | 0.43810 | 0.22919 | |
0.23389 | 0.56190 | 0.77081 | ||
0.38354 | 0.33241 | 0.31570 | 0.30013 | |
4.75877 | 5.23389 | 5.56190 | 5.77081 | |
1.82518 | 1.73980 | 1.75589 | 1.73199 | |
0.34942 | 0.32770 | 0.35934 | 0.29671 | |
0.54883 | 0.50719 | 0.43927 | 0.50577 | |
0.9114 | 0.9304 | 0.9424 | 0.9497 | |
0.91160 | 0.95021 | 0.94241 | 0.95409 | |
0.60903 | 0.24872 | 0.32032 | 0.21333 | |
0.61687 | 0.25656 | 0.32815 | 0.22117 |
9 | 10 | 11 | 12 | |
---|---|---|---|---|
0.27684 | 0.25105 | 0.23882 | 0.24426 | |
0.28342 | 0.30938 | 0.29515 | 0.25907 | |
0.00104 | 0.03261 | 0.01054 | ||
0.05510 | ||||
0.01455 | ||||
0.43974 | ||||
0.43853 | 0.01275 | |||
0.43342 | ||||
0.40373 | ||||
0.01568 | ||||
0.85244 | 0.63676 | 0.43011 | 0.25475 | |
0.13188 | 0.36324 | 0.56989 | 0.73438 | |
0.01087 | ||||
0.27684 | 0.25105 | 0.23882 | 0.24426 | |
6.11620 | 6.36324 | 6.56989 | 6.75612 | |
1.69321 | 1.59749 | 1.56902 | 1.65025 | |
0.28175 | 0.27276 | 0.26535 | 0.25888 | |
0.49128 | 0.46020 | 0.45001 | 0.47176 | |
0.9540 | 0.9558 | 0.9572 | 0.9580 | |
0.97439 | 1.03314 | 1.05356 | 0.99908 | |
0.03046 | 0.47807 | 0.64807 | 0.18689 | |
0.03830 | 0.47023 | 0.64023 | 0.17905 |
15 | 20 | 30 | 50 | |
---|---|---|---|---|
0.23802 | 0.21991 | 0.19606 | 0.17120 | |
0.20997 | 0.23328 | 0.24039 | 0.21053 | |
0.03492 | 0.02058 | 0.00273 | ||
0.12015 | ||||
0.08543 | 0.00228 | |||
0.01587 | 0.06540 | 0.05516 | 0.00009 | |
0.04767 | 0.16602 | 0.15269 | ||
0.01912 | 0.04088 | 0.09227 | ||
0.01064 | 0.02802 | |||
0.00480 | ||||
0.37627 | 0.01206 | |||
0.08064 | ||||
0.22798 | ||||
0.00221 | ||||
0.28636 | 0.07212 | |||
0.25830 | ||||
0.98013 | 0.64854 | 0.00749 | ||
0.01987 | 0.34747 | 0.99101 | 0.33620 | |
0.00399 | 0.00150 | 0.08883 | ||
0.57497 | ||||
0.23802 | 0.21991 | 0.19606 | 0.17120 | |
7.01987 | 7.35545 | 7.99401 | 9.23877 | |
1.67087 | 1.61754 | 1.56731 | 1.58168 | |
0.24945 | 0.24017 | 0.22240 | 0.19699 | |
0.47708 | 0.45783 | 0.44078 | 0.43454 | |
0.9622 | 0.9649 | 0.9690 | 0.9718 | |
0.98692 | 1.01966 | 1.05485 | 1.04429 | |
0.08052 | 0.36399 | 0.65870 | 0.57131 | |
0.07268 | 0.35615 | 0.65086 | 0.56347 |
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Vatta, F.; Babich, F.; Ellero, F.; Noschese, M.; Buttazzoni, G.; Comisso, M. Role of the Product λ′(0)ρ′(1) in Determining LDPC Code Performance. Electronics 2019, 8, 1515. https://doi.org/10.3390/electronics8121515
Vatta F, Babich F, Ellero F, Noschese M, Buttazzoni G, Comisso M. Role of the Product λ′(0)ρ′(1) in Determining LDPC Code Performance. Electronics. 2019; 8(12):1515. https://doi.org/10.3390/electronics8121515
Chicago/Turabian StyleVatta, Francesca, Fulvio Babich, Flavio Ellero, Matteo Noschese, Giulia Buttazzoni, and Massimiliano Comisso. 2019. "Role of the Product λ′(0)ρ′(1) in Determining LDPC Code Performance" Electronics 8, no. 12: 1515. https://doi.org/10.3390/electronics8121515
APA StyleVatta, F., Babich, F., Ellero, F., Noschese, M., Buttazzoni, G., & Comisso, M. (2019). Role of the Product λ′(0)ρ′(1) in Determining LDPC Code Performance. Electronics, 8(12), 1515. https://doi.org/10.3390/electronics8121515