1 Introduction
2 Related work
2.1 Information reconciliation
2.2 Polar codes-based IR schemes
Author | QBER | n | f | \(\varepsilon \) | \(\gamma \) |
---|---|---|---|---|---|
Jouguet and Kunz-Jacques [10] | 0.02 | 64 Kb | 1.395 | 0.090 | 0.731 |
1 Mb | 1.225 | 0.110 | 0.736 | ||
16 Mb | 1.121 | 0.080 | 0.774 | ||
Nakassis and Mink [12] | 0.02 | 64 Kb | 1.425 | 0.073 | 0.740 |
1 Mb | 1.243 | 0.027 | 0.802 | ||
0.04 | 64 Kb | 1.344 | 0.015 | 0.664 | |
1 Mb | 1.188 | 0.031 | 0.690 | ||
0.06 | 64 Kb | 1.247 | 0.068 | 0.552 | |
1 Mb | 1.144 | 0.034 | 0.604 | ||
Yan et al. [11] | 0.02 | 64 Kb | 1.261 | 0.002 | 0.820 |
1 Mb | 1.176 | 0.001 | 0.833 | ||
Our scheme | 0.02 | 1 Mb | 1.146 | \(10^{-8}\) | 0.838 |
16 Mb | 1.085 | \(10^{-8}\) | 0.847 | ||
128 Mb | 1.073 | \(10^{-8}\) | 0.848 | ||
0.04 | 1 Mb | 1.116 | \(10^{-8}\) | 0.730 | |
16 Mb | 1.072 | \(10^{-8}\) | 0.740 | ||
128 Mb | 1.059 | \(10^{-8}\) | 0.743 | ||
0.06 | 1 Mb | 1.099 | \(10^{-8}\) | 0.640 | |
16 Mb | 1.062 | \(10^{-8}\) | 0.652 | ||
128 Mb | 1.049 | \(10^{-8}\) | 0.657 |
3 Shannon-limit approached IR scheme
3.1 Forward reconciliation
3.2 Acknowledgment reconciliation
3.3 Block checked SCL decoder
3.4 Performance of the SLA IR scheme
4 Results
\(E_\mu \) | n=1 Mb | n=16 Mb | n=128 Mb | ||||||
---|---|---|---|---|---|---|---|---|---|
f | \(\varepsilon _\mathrm {f}\) | \(\gamma \) | f | \(\varepsilon _\mathrm {f}\) | \(\gamma \) | f | \(\varepsilon _\mathrm {f} \) | \(\gamma \) | |
0.01 | 1.205 | 0.0164 | 0.903 | 1.114 | 0.0032 | 0.910 | 1.091 | \(\le 10^{-4}\) | 0.912 |
0.02 | 1.146 | 0.0050 | 0.838 | 1.085 | 0.0138 | 0.847 | 1.073 | \(\le 10^{-4}\) | 0.848 |
0.03 | 1.124 | 0.0163 | 0.782 | 1.087 | 0.0005 | 0.789 | 1.062 | 0.0011 | 0.794 |
0.04 | 1.116 | 0.0072 | 0.730 | 1.072 | 0.0048 | 0.740 | 1.059 | 0.0033 | 0.743 |
0.05 | 1.107 | 0.0046 | 0.683 | 1.070 | 0.0022 | 0.694 | 1.055 | \(\le 10^{-4}\) | 0.698 |
0.06 | 1.099 | 0.0040 | 0.640 | 1.062 | 0.0050 | 0.652 | 1.049 | 0.0067 | 0.657 |
0.07 | 1.101 | 0.0012 | 0.597 | 1.066 | 0.0004 | 0.610 | 1.050 | \(\le 10^{-4}\) | 0.616 |
0.08 | 1.104 | 0.0026 | 0.556 | 1.064 | 0.0001 | 0.572 | 1.048 | \(\le 10^{-4}\) | 0.579 |
0.09 | 1.092 | 0.0037 | 0.523 | 1.056 | 0.0007 | 0.539 | 1.044 | 0.0015 | 0.544 |
0.1 | 1.083 | 0.0064 | 0.492 | 1.062 | \(\le 10^{-4}\) | 0.502 | 1.042 | \(\le 10^{-4}\) | 0.511 |
0.11 | 1.079 | 0.0024 | 0.461 | 1.057 | \(\le 10^{-4}\) | 0.472 | 1.039 | 0.0050 | 0.481 |
0.12 | 1.072 | 0.0043 | 0.433 | 1.056 | \(\le 10^{-4}\) | 0.441 | 1.037 | 0.0013 | 0.451 |