Simulation Results
5.1 The Path Deletion Schemes in Chapter 3
In this section, we examine the path deletion schemes we proposed in Chapter 3. Also examined is the path deletion scheme that uses the Fano metric to select the top path to be extended, and to delete the path when the stack is full. This scheme is referred to as Fano metric delete by Fano metric in the legend. By following similar naming rule, the Fano metric-based path deletion scheme is referred to as MLSDA delete by Fano metric, and the level-based path deletion scheme is briefed as MLSDA delete by path level in the legend. The ML metric-based path deletion scheme is likewisely referred to as MLSDA delte by Wagner metric.
We compare these path deletion schemes using (2, 1, 8) convolutional codes with generator polynomial [457,755] (in octal) and (2, 1, 12) convolutional codes with generator polynomial [17663,11271] (in octal). Simulations for (2, 1, 8) convolutional code are summarized in Fig-ures 5.1–5.9.
Figures 5.1–5.6 show that Fano metric-based path deletion scheme is the best in error performance when the stack size is upper-bounded by 26−1 and 28−1. The ML metric-based path deletion scheme performs apparent worse than all the other schemes, and also requires the largest computational complexity. More specifically, we observe from Figure 5.1 that the word error rate (WER) of the MLSDA delete by Fano Metric performs 0.5 dB better than the MLSDA delete by level when the stack size is limited to 26− 1. In comparison with the Fano metric delete by Fano metric, MLSDA delete by Fano Metric is still 0.2 dB superior in WER performance. However, Figure 5.3 shows that the computational complexity of the MLSDA delete by Fano Metric is around two times larger than both Fano metric delete by Fano metric and MLSDA delete by level. This leads to a tradeoff between error rate and computational complexity when one wishes to select among these schemes.
When the stack size is enlarged to a big size, e.g., 216− 1, Figures 5.7–5.9 show that near optimal performance can be achieved by all three schemes we proposed in Chapter 3. Yet, with a large stack size, the average computational complexity of the three proposed schemes will become much larger than Fano metric delete by Fano metric.
For (2,1,12) convolutional codes with generator polynomial [17663,11271] (in octal), we observe from Figures 5.10–5.15 that the proposed MLSDA delete by Fano Metric is still the best in error performance when stack size is limited to 212− 1, but its computational complexity is again higher than Fano metric delete by Fano metric and MLSDA delete by level. Figures 5.13–5.15 indicates that optimality can be achieved when the stack size further increases up to 216− 1.
From the above simulations, we conclude that Fano metric-based path deletion scheme can achieve better performance when the memory saving is critical in the system design.
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3 10−3
10−2 10−1 100
Eb/N0
WER
MLSDA delete by Fano metric MLSDA delete by path level MLSDA delete by Wagner metric Fano metric delete by Fano metric ML
Figure 5.1: Word error rate (WER) performance of path deletion schemes for (2,1,8) convolu-tional code with generator polynomial [457,755]. The stack size is 26−1, and the information sequence length L = 100.
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3 10−4
10−3 10−2 10−1 100
Eb/N0
BER
MLSDA delete by Fano metric MLSDA delete by path level MLSDA delete by Wagner metric Fano metric delete by Fano metric ML
Figure 5.2: Bit error rate (BER) performance of path deletion schemes for (2,1,8) convolu-tional code with generator polynomial [457,755]. The stack size is 26−1, and the information sequence length L = 100.
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3 0
10 20 30 40 50 60 70 80 90
Eb/N0
Average computational complexity per information bit
MLSDA delete by Fano metric MLSDA delete by path level MLSDA delete by Wagner metric Fano metric delete by Fano metric
Figure 5.3: Average computational complexity per information bit of path deletion schemes for (2,1,8) convolutional code with generator polynomial [457,755]. The stack size is 26− 1, and the information sequence length L = 100.
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3 10−5
10−4 10−3 10−2
Eb/N0
WER
MLSDA delete by Fano metric MLSDA delete by path level MLSDA delete by Wagner metric Fano metric delete by Fano metric ML
Figure 5.4: Word error rate (WER) performance of path deletion schemes for (2,1,8) convolu-tional code with generator polynomial [457,755]. The stack size is 28−1, and the information sequence length L = 100.
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3 10−6
10−5 10−4 10−3 10−2
Eb/N0
BER
MLSDA delete by Fano metric MLSDA delete by path level MLSDA delete by Wagner metric Fano metric delete by Fano metric ML
Figure 5.5: Bit error rate (BER) performance of path deletion schemes for (2,1,8) convolu-tional code with generator polynomial [457,755]. The stack size is 28−1, and the information sequence length L = 100.
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3
Average computational complexity per information bit
MLSDA delete by Fano metric MLSDA delete by path level MLSDA delete by Wagner metric Fano metric delete by Fano metric
Figure 5.6: Average computational complexity per information bit of path deletion schemes for (2,1,8) convolutional code with generator polynomial [457,755]. The stack size is 28− 1, and the information sequence length L = 100.
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3 10−5
10−4 10−3 10−2
Eb/N0
WER
MLSDA delete by Fano metric MLSDA delete by path level MLSDA delete by Wagner metric Fano metric delete by Fano metric ML
Figure 5.7: Word error rate (WER) performance of path deletion schemes for (2,1,8) con-volutional code with generator polynomial [457,755]. The stack size is 216 − 1, and the information sequence length L = 100.
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3 10−6
10−5 10−4 10−3
Eb/N0
BER
MLSDA delete by Fano metric MLSDA delete by path level MLSDA delete by Wagner metric Fano metric delete by Fano metric ML
Figure 5.8: Bit error rate (BER) performance of path deletion schemes for (2,1,8) convolu-tional code with generator polynomial [457,755]. The stack size is 216−1, and the information sequence length L = 100.
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3 0
50 100 150 200 250 300
Eb/N0
Average computational complexity per information bit
MLSDA delete by Fano metric MLSDA delete by path level MLSDA delete by Wagner metric Fano metric delete by Fano metric
Figure 5.9: Average computational complexity per information bit of path deletion schemes for (2,1,8) convolutional code with generator polynomial [457,755]. The stack size is 216− 1, and the information sequence length L = 100.
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3 10−6
10−5 10−4 10−3 10−2
Eb/N0
WER
MLSDA delete by Fano metric MLSDA delete by path level MLSDA delete by Wagner metric Fano metric delete by Fano metric ML
Figure 5.10: Word error rate (WER) performance of path deletion schemes for (2,1,12) convolutional code with generator polynomial [17663,11271]. The stack size is 212− 1, and the information sequence length L = 100.
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3 10−7
10−6 10−5 10−4 10−3 10−2
Eb/N0
BER
MLSDA delete by Fano metric MLSDA delete by path level MLSDA delete by Wagner metric Fano metric delete by Fano metric ML
Figure 5.11: Bit error rate (BER) performance of path deletion schemes for (2,1,12) convo-lutional code with generator polynomial [17663,11271]. The stack size is 212− 1, and the information sequence length L = 100.
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3 0
500 1000 1500 2000 2500 3000
Eb/N0
Average Complexity per information bit
MLSDA delete by Fano metric MLSDA delete by path level MLSDA delete by Wagner metric Fano metric delete by Fano metric
Figure 5.12: Average computational complexity per information bit of path deletion schemes for (2,1,12) convolutional code with generator polynomial [17663,11271]. The stack size is 212− 1, and the information sequence length L = 100.
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3 10−4
10−3 10−2 10−1 100
Eb/N0
WER
MLSDA delete by Fano metric MLSDA delete by path level MLSDA delete by Wagner metric Fano metric delete by Fano metric ML
Figure 5.13: Word error rate (WER) performance of path deletion schemes for (2,1,12) convolutional code with generator polynomial [17663,11271]. The stack size is 216− 1, and the information sequence length L = 100.
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3 10−5
10−4 10−3 10−2 10−1
Eb/N0
BER
MLSDA delete by Fano metric MLSDA delete by path level MLSDA delete by Wagner metric Fano metric delete by Fano metric ML
Figure 5.14: Bit error rate (BER) performance of path deletion schemes for (2,1,12) convo-lutional code with generator polynomial [17663,11271]. The stack size is 216− 1, and the information sequence length L = 100.
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3 0
500 1000 1500 2000 2500 3000 3500 4000
Eb/N0
Average computational complexity per information bit
MLSDA delete by Fano metric MLSDA delete by path level MLSDA delete by Wagner metric Fano metric delete by Fano metric
Figure 5.15: Average computational complexity per information bit of path deletion schemes for (2,1,12) convolutional code with generator polynomial [17663,11271]. The stack size is 216− 1, and the information sequence length L = 100.