Numerical Results and Related Discussions
5.2 Simulation Results
Computer-simulated bit error rate (BER) and frame error rate (FER) performance of two different puncturing schemes for LDPC codes are reported in this section. One scheme is proposed in paper [7] and another is proposed scheme. The (576, 192) 2/3-rate LDPC code defined in 2005-802.11n, the PEG (504,252) 0.5-2/3-rate LDPC code and the (1920, 640) 1/3-rate Gallager LDPC code are used in simulations. Sum product decoding algorithm is taken and the maximum number of iteration is set to be 100.
Figure 5.37 depicts the BER performance of the QC code. When the puncturing code rate is 3/4, 4/5 and 5/6, the proposed scheme outperforms [7] by about 0.24 dB at BER=3∗ 10−6, 0.25 dB at BER=6∗ 10−6 and 0.875 dB at BER= 10−5, respectively.
Figure 5.38 depicts the FER performance of the QC code. When the puncturing code rate achieves 3/4, 4/5 and 5/6, the proposed scheme offers about 0.24 dB gain around FER=10−4, 0.26 dB gain at FER=2∗ 10−4 and 1 dB gain at FER= 4∗ 10−4 against [7], respectively.
Figure 5.39 depicts the BER performance of the PEG code. When the puncturing code rate is 2/3 and 3/4, the proposed scheme outperforms [7] with 0.1 dB distance at BER=6∗ 10−6 and 1 dB distance at BER=2∗ 10−5, respectively.
Figure 5.1: Ratio of SR order and the number and the degree of SCN. (QC576 R=3/4)
Figure 5.2: Average number of un-/punctured nodes which a SCN connects. (QC576 R=3/4)
Figure 5.3: The percentage of the number of SCN. (QC576 R=3/4)
1 2
Figure 5.4: recovery error probability (QC576 R=3/4)
1 2 3 4 5 6 7 8 9 10
Figure 5.5: BER with iterations (QC576 R=3/4)
0 1 2
Figure 5.6: BER at 100th iteration (QC576 R=3/4)
Figure 5.7: Ratio of SR order and the number and the degree of SCN. (QC576 R=4/5)
Figure 5.8: Average number of un-/punctured nodes which a SCN connects. (QC576 R=4/5)
Figure 5.9: (In detail) Average number of punctured nodes which a SCN connects.
(QC576 R=4/5)
Figure 5.10: Average number of neighboring punctured nodes of 1-SR. (QC576 R=4/5)
Figure 5.11: The percentage of the number of SCN. (QC576 R=4/5)
1 2 3 4
Figure 5.12: recovery error probability (QC576 R=4/5)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Figure 5.13: BER with iterations (QC576 R=4/5)
0 1 2 3 4
Figure 5.14: BER at 100th iteration (QC576 R=4/5)
Figure 5.15: Ratio of SR order and the number and the degree of SCN. (QC576 R=5/6)
Figure 5.16: Average number of un-/punctured nodes which a SCN connects. (QC576 R=5/6)
Figure 5.17: (In detail) Average number of punctured nodes which a SCN connects.
(QC576 R=5/6)
Figure 5.18: Average number of neighboring punctured nodes of 1-SR. (QC576 R=5/6)
P t f th b f SCN f diff t SR d
1ͲSR 2ͲSR 3ͲSR 4ͲSR 5ͲSR 6ͲSR 4
1ͲSR 2ͲSR 3ͲSR 4ͲSR 5ͲSR 6ͲSR
Figure 5.19: The percentage of the number of SCN. (QC576 R=5/6)
0 1 2 3 4 5 6
Figure 5.20: recovery error probability (QC576 R=5/6)
1 2 3 4 5 6 7 8 9 10
Figure 5.21: BER with iterations (QC576 R=5/6)
0 1 2 3 4 5 6 1E-5
1E-4 1E-3 0.01
QC 576 R=2/3 to 5/6 SNR=5
BER at 100th iteration
Recovery Order
paper [7]
Proposed Scheme
Figure 5.22: BER at 100th iteration (QC576 R=5/6)
Figure 5.23: Ratio of SR order and the number and the degree of SCN. (PEG504 R=2/3)
Figure 5.24: Average number of un-/punctured nodes which a SCN connects. (PEG504 R=2/3)
Percentage of the number of SCN
Figure 5.25: The percentage of the number of SCN. (PEG504 R=2/3)
1 2 3
Figure 5.26: recovery error probability (PEG504 R=2/3)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Figure 5.27: BER with iterations (PEG504 R=2/3)
0 1 2 3 1E-5
1E-4 1E-3
PEG 504 R=1/2 to 2/3 SNR=3.75
BER at 100th iteration
Recovery Order
paper [7]
Proposed Scheme
Figure 5.28: BER at 100th iteration (PEG504 R=2/3)
Figure 5.29: Ratio of SR order and the number and the degree of SCN. (PEG504 R=3/4)
Figure 5.30: Average number of un-/punctured nodes which a SCN connects. (PEG504 R=3/4)
Figure 5.31: (In detail) Average number of punctured nodes which a SCN connects.
(PEG504 R=3/4)
Figure 5.32: Average number of neighboring punctured nodes of 1-SR. (PEG504 R=3/4)
Percentage of the number of SCN Paper[7]
1ͲSR 2ͲSR 3ͲSR 4ͲSR 5ͲSR 6ͲSR 7ͲSR 8ͲSR 4
1ͲSR 2ͲSR 3ͲSR 4ͲSR 5ͲSR 6ͲSR 7ͲSR
Figure 5.33: The percentage of the number of SCN. (PEG504 R=3/4)
1 2 3 4 5 6 7 8
Figure 5.34: recovery error probability (PEG504 R=3/4)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Figure 5.35: BER with iterations (PEG504 R=3/4)
0 1 2 3 4 5 6 7 8
Figure 5.36: BER at 100th iteration (PEG504 R=3/4)
Figure 5.40 depicts the FER performance of the PEG code. When the puncturing code rate achieves 2/3 and 3/4, the proposed scheme yields 0.2 dB gain around FER=2∗ 10−4 and 1.2 dB gain at FER=6.5∗ 10−4 against [7], respectively.
Figure 5.41 depicts the BER performance of the Gallager code. When the puncturing code rate is 2/3, the proposed scheme outperforms [7] by about 0.4 dB at BER=10−4. Figure 5.42 depicts the FER performance of the code. When the puncturing code rate is 2/3, the proposed scheme offers about 0.4 dB gain around FER=10−3 against [7].
2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0
Figure 5.37: BER performance of puncturing QC code
2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0
Figure 5.38: FER performance of puncturing QC code
1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5
Figure 5.39: BER performance of puncturing PEG code
1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5
Figure 5.40: FER performance of puncturing PEG code
1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2 1E-4
1E-3 0.01
Gallager 1920
BER
SNR
Paper [7] (R=1/2) Proposed Scheme (R=1/2) Paper [7] (R=2/3) Proposed Scheme (R=2/3)
Figure 5.41: BER performance of puncturing Gallager code with mother code rate 1/3
1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2
1E-3 0.01 0.1
Gallager 1920
FER
SNR
Paper [7] (R=1/2) Proposed Scheme (R=1/2) Paper [7] (R=2/3) Proposed Scheme (R=2/3)
Figure 5.42: FER performance of puncturing Gallager code with mother code rate 1/3
Chapter 6 Conclusions
We present a puncture pattern design scheme for finite-length LDPC codes. For use in AWGN channels, we use GA to analyze the error probability of variable nodes. Some indicator parameters associated with the recovery capability of punctured nodes and the error-correcting performance of unpunctured nodes are obtained based on the analysis.
The design guidelines are derived from the relationships between these parameters and error-rate performance. We also compare the decoding performance of our scheme with that of existing approaches. The experimental results prove that the performance of the proposed algorithm does offer better performance in comparison with the method in [7], which is consistent with the GA-based theoretical prediction.
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