Performance Evaluation Over the Punctured Codes
5.2 Performance of Punctured Codes
Fig. 5.3 and Fig. 5.4 summarize the simulated performance of codes with different cod-ing rates under the AWGN channel for symbol-based ML decision in (2.1), the proposed bit-decomposed metrics, the soft-demapping in Chapter 2.3.1, the simplified bit metrics in Chapter 2.3.2, and the straightforward hard-decision decoding system. As stated in the pre-vious chapter, they are respectively abbreviated as Symbol-ML, Soft-proposed, Soft-demap, Soft-TB and Hard in all subsequent figures. Under 16QAM modulation and at BER = 10−5, for coding rates 1/2, 2/3, and 3/4, Soft-proposed (equivalently, Soft-TB) has 3.0 dB, 2.7 dB, and 2.6 dB gain over Hard respectively. Under 64QAM modulation and at BER = 10−5, for coding rates 1/2, 2/3, and 3/4, Soft-proposed (equivalently, Soft-TB) has 3.9 dB, 3.0 dB, and 2.8 dB gain over Hard respectively. Under 256QAM modulation and at BER = 10−5, for coding rates 1/2, 2/3, and 3/4, Soft-proposed (equivalently, Soft-TB) has 5.1 dB, 3.7 dB, and 3.3 dB gain over Hard respectively. One can see that, with the higher puncture cod-ing rate, the codcod-ing gain reduces. Furthermore, the three soft-decision decodcod-ing algorithms considered have similar performance when higher puncture coding rates are employed.
1e-07
Figure 5.3: System performance of punctured codes with different coding rates under the AWGN channel for 16QAM and 64QAM modulations.
1e-07
Figure 5.4: System performance of punctured codes with different coding rates under the AWGN channel for 256QAM modulation.
There are several rate-dependent parameters recommended in the standard of IEEE 802.11a/g [11, 12] (see Table 5.1). However, there are still some alternatives. For example, the punctured code with coding rate 1/2 under 64QAM modulation has the same information bit rate as the punctured code with coding rate 3/4 under 16QAM modulation that is recommended in the standard. Furthermore, the punctured code with coding rate 1/2 under 256QAM modulation has the same information bit rate as the punctured code with coding rate 2/3 under 64QAM modulation that is recommended in the standard. In the following we will investigate the BER performance of all codes recommended in the standard under 16QAM and 64QAM modulations and the above two alternatives.
Fig. 5.5 illustrates the BER performance of punctured codes for Hard and Soft-demap under the AWGN channel for 16QAM, 64QAM, and 256QAM modulations. Under 16QAM modulation and at BER = 10−5, the punctured code with coding rate 3/4 has 0.9 dB and 0.56 dB gain over the code with coding rate 1/2 under 64QAM modulation for Hard and
Soft-Table 5.1: Rate-dependent parameters in the std. of IEEE 802.11a/g Date − rate Modulation Coding Coded − bits Coded − bits Data − bits
rate per per − OF DM per − OF DM subcarrier symbol symbol
(Mbits/s) (R) (NBP SC) (NCBP S) (NDBP S)
6 BPSK 1/2 1 48 24
9 BPSK 3/4 1 48 36
12 QPSK 1/2 2 96 48
18 QPSK 3/4 2 96 72
24 16QAM 1/2 4 192 96
36 16QAM 3/4 4 192 144
48 64QAM 2/3 6 288 192
54 64QAM 3/4 6 288 216
demap, respectively. At the same bit error rate, under 64QAM modulations the punctured code with coding rate 2/3 has 2.6 dB and 2.1 dB gain over that with coding rate 1/2 under 256QAM modulation for Hard and Soft-demap, respectively. Hence, the code with rate 1/2 under 64QAM modulation can be replaced by the code with coding rate 3/4 under 16QAM modulation. Similarly, the code with coding rate 1/2 under 256QAM can be replaced by the code with code rate 2/3 under 64QAM modulation. These results reveal that the codes recommended in the standard indeed superior to the above two alternatives for Hard and Soft-demap.
Fig. 5.6 presents the BER performance of punctured codes for proposed and Soft-TB under the AWGN channel for 16QAM, 64QAM, and 256QAM modulations. At BER
= 10−5, under 64QAM modulation the code with coding rate 1/2 has 0.33 dB gain over that with coding rate 3/4 under 16QAM modulation for Soft-proposed and Soft-TB. This indicates that, when employing Soft-proposed or Soft-TB, the code with coding rate 1/2 under 64QAM modulation is preferred to the code with rate 3/4 under 16QAM modulation recommended in the standard. At the same bit error rate, the code with code rate 2/3
under 64QAM modulation recommended in the standard still has 0.67 dB gain over that with coding rate 1/2 under 256QAM modulation for Soft-proposed and Soft-TB.
Fig. 5.7 summarizes the BER performance of punctured codes with different coding rates under the Rayleigh flat fading channel for Symbol-ML, Soft-proposed, Soft-demap, Soft-TB and Hard. Under 16QAM modulation and at BER = 10−5, for coding rates 1/2, 2/3, and 3/4, Soft-proposed (equivalently, Soft-TB) has 7.7 dB, 10.4 dB, and 13.0 dB gain over Hard respectively. Under 64QAM modulation and at BER = 10−5, for coding rates 1/2, 2/3, and 3/4, Soft-proposed (equivalently, Soft-TB) has 8.1 dB, 10.7 dB, and 13.3 dB gain over Hard, respectively. In contrast to the cases under the AWGN channel, with the higher puncture coding rate the coding gain increases under the Rayleigh flat fading channel.
Furthermore, unlike the cases under the AWGN channel, the three soft-decision decoding algorithms considered have quite different performance when higher puncture coding rates are employed under the Rayleigh flat fading channel.
Fig. 5.8 and Fig. 5.9 illustrate the BER performance of punctured codes for Hard, Soft-demap, Soft-proposed, and Soft-TB under the Rayleigh flat fading channel for 16QAM and 64QAM modulations. Under 64QAM modulation and at BER = 10−5, the punctured code with coding rate 1/2 has 9.3 dB, 8.3 dB, and 5.1 dB gain over the code with coding rate 3/4 under 16QAM modulation for Hard, Soft-demap, Soft-proposed, and Soft-TB, respectively.
This indicates that, when under the Rayleigh flat fading channel, employing not only Soft-proposed or Soft-TB but also Soft-demap and Hard, the code with coding rate 1/2 under 64QAM modulation is preferred to the code with rate 3/4 under 16 QAM modulation.
1e-07
Figure 5.5: System performance of punctured codes with different coding rates under the AWGN channel for Hard and Soft-demap.
1e-07
Figure 5.6: System performance of punctured codes with different coding rates under the AWGN channel for Soft-proposed and Soft-TB.
1e-07
Figure 5.7: System performance of punctured codes with different coding rates under the Rayleigh flat fading channel for 16QAM and 64QAM modulations.
1e-06
Figure 5.8: System performance of punctured codes with different coding rates under the Rayleigh flat fading channel for Hard and Soft-demap.
1e-07
Figure 5.9: System performance of punctured codes with different coding rates under the Rayleigh flat fading channel for Soft-proposed and Soft-TB.