On the Achievable Information Rate of Probabilistic Shaping QAM Order and Source Entropy in Visible Light Communication Systems

Round 1

Reviewer 1 Report

This paper investigates a relationship between QAM order, SE, NGMI, and AIR in the PS-CAP VLC system. The authors proposed a PS QAM order and SE selection scheme that can realize a high AIR at the lowest computation complexity with a proper NGMI threshold. It seems good to have done a lot of experiments to show what they claims but, several problems exist for this paper. 

 

(1) Many parts of English expression and grammar are wrong. 

(2) In section 2, the description of the related formula and some notations are missing. 

(3) In section 3, there is a lack of specific setting and explanations for Fig.1. 

(4) Most simulation results in Figures cannot be distinguished for black and white prints.

 

In addition, what is different between two subsections of simulation and experiment in section 4? 

 

Author Response

Point 1: Many parts of English expression and grammar are wrong.


 

Response 1:

Thanks for your kind comments. There are some places that the grammar and expression are not reasonable. We have corrected the mistakes in the ‘Trach changes’ manuscript and listed them as follow:

(1). Line 96-98:

In this paper, we utilize the famous probabilistic amplitude shaping (PAS) system with MB distribution to realize the PS scheme.

(2). Line 123-124:

The SE of each PS QAM order is increased by 0.1 bit/symbol to find the highest AIR (HAIR) of each PS constellation when .

(3). Line 184-186:

…The higher the QAM order, the more redundant bits the FEC code introduces, thereby introducing higher system delay….

(4). Line 188 to 189:

First, the simulation results are carried out in the AWGN channel. The SE and optimal AIR which just satisfy the 0.92 NGMI threshold at different SNR are shown in Fig. 3.

(5). Line 199 to 204:

The SE and optimal AIR which just satisfy the 0.86 NGMI threshold at different SNR are shown in Fig. 4. The transition SNR for QAM orders 6 to 7 and 7 to 8 are 15.65 dB and 17.63 dB respectively. As the FEC code rate decreases, higher SE is permitted to transmit more bits in the channel. Furthermore, the AIR performance of 256QAM and 512QAM are very close to each other. Similar to the results in Fig. 3, it is not necessary to implement 512QAM in the simulation.

(6). Line 208:

The optimal HAIR performance of different QAM orders at different SNR is shown in Fig. 5(a).

(7). Line 219:

Table 2àTable 1.

(8). Line 220-221:

Then we simulated the performance of the CAP based VLC system. First, the SNR performance in the CAP based VLC system is measured.

(9). Line 224:

Fig. 5àFig. 6;

(10). Line 226:

the SNR of the PS signal.

(11). Line 231-232:

Then the NGMI and AIR performance with SE according to Fig. 3-5 (b) are shown in Fig. 7(a) and Fig. 7(b) respectively.

(12). Line 236:

The AIR is shown in Fig. 7(b) and …

(13). Line 259:

The ‘GMI’ is deleted.

(14). Line 267:

The measured NGMI of PS constellations are all above the 0.92 NGMI threshold and the maximum NGMI is 0.924.

(15). Line 269-270:

Therefore, the simulation results match well with the experimental results, which proves that the PS mapping scheme is feasible.

(16). Line 281:

…is feasible for AIR improvement of the PS signal….

 

 

Point 2: In section 2, the description of the related formula and some notations are missing.

 

Response 2:

Thanks for your very constructive comments. The related formula and some notations are listed as follow:

(1). Line 89:

Where SNR is measured by the training sequence. It has been proved that for the QAM constellations, …

(2). Line 95-98:

Where  is the shaping factor of PS. The larger the  is, the greater the difference in probability between the inner and outer circles of the constellation points. In this paper, …

(3). Line 99-100:

As GMI and NGMI can effectively reflect the decoding performance of soft decision-LDPC (SD-LDPC) in the PAS system, we will utilize them as the metrics in this study.

(4). Line 110-111:

The normalized GMI (NGMI) reflects the ideal binary FEC rate of the system for error-free transmission. For M QAM PAS with LDPC encoding procedure, …

(5). Line 121-122:

In this paper, we compared the simulation results of NGMI for different PS QAM orders at the same AIR and the same preset NGMI threshold

 

Point 3: In section 3, there is a lack of specific setting and explanations for Fig.1.

 

Response 3:

Thanks for your constructive comments.

The detailed parameters for setting are listed in Table. 1. Furthermore, we have appended the references for CAP in Line 141: For more details of CAP, please refer to article [3].

 

Point 4: Most simulation results in Figures cannot be distinguished for black and white prints.

 

Response 4:

Thanks for your constructive comments.

We have changed the line styles in Fig. 3-7 to ensure that the results can be distinguished for black and white prints.

 

Point 5: In addition, what is different between two subsections of simulation and experiment in section 4?.

 

Response 5:

Thanks for your kind comments.

The differences are listed as follow:

(i). The VLC channel of simulation is a simple exponential fading channel with additive white gaussian noise (AWGN). While the channel of the experiment is more complex than that of simulation because of the complex frequency and time domain response between the transmitting signal and the receiving signal. Therefore, the simulation results should be verified in an experiment.

(ii). We simulated 3 scenarios in this paper, which is the 0.86 NGMI threshold (scenario (1), corresponds to 5/6 code rate), 0.92 NGMI threshold (scenario (2). corresponds to code rate 9/10) and dynamic NGMI threshold (scenario (3)). In the experiment, scenario (3) is not measured as adjusting code rate by the system SNR is not practical for LDPC.

(iii). The source entropy of the experiment is subtracted by 0.1 bpQs for each SNR compared to that of simulation. This operation is processed to ensure error-free decoding for the PAS system.

We have verified the first paragraph of Section 4.2:

In Section 4.1, we have verified the performance of our proposed PS scheme on the simulation platform. However, the channel of the experimental platform is much more complicated than that of the simulation platform. Therefore, it is necessary to further verify the performance of the proposed PS scheme on the VLC experimental setup. Since the code rate of scenario 3 needs to be dynamically adjusted according to SNR, which is impossible to achieve in the actual system, we only tested the performance under the two thresholds of 0.86 and 0.92 on the experimental setup. To ensure the system meets the NGMI threshold, we choose to subtract the achieved SE by 0.1 bpQs.

Author Response File: Author Response.docx

Reviewer 2 Report

In this manuscript, the authors study the relationship between PS QAM order, SE, NGMI, and AIR performance for visible light communication system. The simulation and experimental results show that the proposed scheme in the paper can meet the NGMI threshold. 

I would recommend the authors expand the conclusion section to provide a more comprehensive overview of the work presented in the paper and provide more details for future work and enhancements.

Author Response

Point 1: I would recommend the authors expand the conclusion section to provide a more comprehensive overview of the work presented in the paper and provide more details for future work and enhancements.


 

Response 1:

Thanks for your kind comments. We have appended some sentences to illustrate more details for the future work and overview of the work in Section 5. The changes are listed as follow:

In this paper, we investigated for the first time the relationship between QAM order, SE, NGMI, and AIR in the PS-CAP VLC system. Simulation and experimental results demonstrate that with the aid of the proposed scheme in this paper, we can meet the NGMI threshold with the lowest computation complexity. Compared with the highest AIR, the AIR loss proposed in this paper is only 0.1 bpQs. Simulation results show that the NGMI only fluctuates within the range of ±0.004 around the preset NGMI threshold. Experimental results show that the NGMI are all above the preset NGMI threshold and only fluctuate within a small range by subtracting 0.1 bpQs SE. Therefore, the scheme proposed in this paper is feasible for AIR improvement of the PS signal. Furthermore, with the scheme proposed in this paper, a very high AIR without coding redundancy can be achieved at the lowest cost according to the channel SNR, which only has a 0.1 bpQs gap at most to the largest AIR of the system. Consequently, the scheme proposed in this paper has great potential in standardizing communication systems. In this study, the Vpp is adjusted in a small range to suppress the nonlinear distortion. In the future, the AIR-based PS scheme in the nonlinear VLC system needs to be investigated. Besides, the performance of the proposed PS scheme needs to be verified in the multi-input multi-output (MIMO) VLC system as well.

Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

(1) I still see a lot of errors in grammar. 

(2) Most figures (ex, Fig. 3 (a) and (b), Fig. 4 (a) and (b)) are still hard to be distinguished for black and white prints.

(3) In every equation, there is no comma(,) or a period (.). Further, it is wrong that "Where" after the expression where the capital letter begins. 

 

Author Response

Response to Reviewer 1 Comments

 

 

 

Point 1: I still see a lot of errors in grammar.

 

Response 1:

Thanks for your kind comments. We have carefully modified the grammar according to the advice of peers and professional grammar software ‘Grammarly’. We listed the revisions as follow:

• Line 32-35:

Before: …However, traditional QAM has two apparent disadvantages: First, traditional QAM has a coarse granularity in spectral efficiency, which cannot adapt the system data rate to the channel signal to noise ratio (SNR) at a fine granularity [7]….

After: …However, traditional QAM has two apparent disadvantages: First, traditional QAM has a coarse granularity in spectral efficiency, which cannot make full use of the channel capacity[7]….

• Line 63:

Before: …which is a very important issue…

After: …which is a fundamental issue…

• Line 67-68:

Before: …the VLC system is different from the fiber system, the performance of PS need to be verified…

After: …the VLC system is different from the fiber system and the performance of PS need to be verified

• Line 71-72:

Before: …there is little research on the selection of PS QAM order and SE which can meet the specific NGMI threshold with high AIR.

After: …there is little research on the selection of PS QAM order and SE, which can meet the specific NGMI threshold with high AIR.

• Line 74-76：

Before: …According to the channel SNR which is measured by the uniform 64QAM and the proposed schemes in this paper, the SE can be adjusted to meet the NGMI threshold.

After: …According to the channel SNR and the proposed schemes, the SE can be adjusted to meet the NGMI threshold….

• Line 98-99:

Before: …As GMI and NGMI can effectively reflect the decoding performance…

After: …As GMI and NGMI can adequately reflect the decoding performance…

• Line 141:

Before: …For more details of CAP, please refer to article[3]….

After: …For more details of CAP, please refer to the article[3]….

• Line 151-153:

Before: …while the processing after CAP modulation and before CAP demodulation is replaced by the simulation VLC channel….

After: …while the simulation VLC channel replaces the processing after CAP modulation and before CAP demodulation….

• Line 174:

Before: …we try to find the QAM order and SE which owns big enough AIR…

After: …we try to find the QAM order and SE, which owns big enough AIR…

• Line 177:

Before: …order which owns a much lower computation complexity…

After: …order, which owns a much lower computation complexity…

• Line 180:

Before: …4.99×10¹⁷ respectively.…

After: …4.99×10¹⁷, respectively….

• Line 187:

Before: …First, the simulation results are carried out in the AWGN channel….

After: …First, the simulation results are carried out on the AWGN channel….

• Line 187-188:

Before: …The SE and optimal AIR which just satisfy the 0.92 NGMI threshold at different SNR are shown in Fig. 3….

After: …The SE and optimal AIR satisfy the 0.92 NGMI threshold at different SNR are shown in Fig. 3….

• Line 189-190:

Before: …However, as raising one order will inevitably increasing the computation complexity to a big degree,…

After: …However, as raising one order will inevitably increasing the computation complexity significantly,…

• Line 198:

Before: …The SE and optimal AIR which just satisfy the 0.86 NGMI threshold at different SNR are shown

After: …The SE and optimal AIR satisfy the 0.86 NGMI threshold at different SNR are shown…

• Line 199:

Before: …The transition SNR from QAM orders 6 to 7 and 7 to 8 are 15.65 dB and 17.63 dB respectively.

After: …The transition SNR from QAM orders 6 to 7 and 7 to 8 are 15.65 dB and 17.63 dB, respectively.

• Line 206:

Before: …The optimal HAIR performance of different QAM orders at different SNR is shown in Fig. 5(a)….

After: …The optimal HAIR performance is shown in Fig. 5(a)….

• Line 209-210:

Before: …This is different from scenario 1 and 2…

After: …This operation is different from scenario 1 and 2…

• Line 210:

Before: …SNR are 15.78 dB and 17.51 dB respectively….

After: …SNR are 15.78 dB and 17.51 dB, respectively….

• Line 216-217:

Before: …The QAM order exchanging point of scenario 1 to 3 is summarized in Table. 1.

After: …Table. 1 summarized the QAM order exchanging point of scenario 1 to 3…

• Line 220-221:

Before: …As channel SNR is measured by the training sequence, it is important to know the relationship

After: …As the training sequence measures the channel SNR, it is crucial to know the relationship…

• Line 237:

Before: …Therefore, for a practical system,…

After: …Therefore, for a functional system,…

• Line 247:

Before: …Therefore, it is necessary to further verify the performance…

After: …Therefore, it is necessary to verify the performance…

• Line 248-250:

Before: …Since the code rate of scenario 3 needs to be dynamically adjusted according to SNR, …

After: …Since we need to adjust the code rate according to the measured SNR in scenario 3,

• Line 255:

Before: …achieved by the measured SNR and are shown…

After: …achieved by the measured SNR and shown

• Line 266:

Before: …above the 0.92 NGMI threshold and the maximum NGMI is 0.924…..

After: …above the 0.92 NGMI threshold, and the maximum NGMI is 0.924….

• Line 279:

Before: …and only fluctuate within a small range by subtracting 0.1 bpQs SE…..

After: …and only vary within a small scale by subtracting 0.1 bpQs SE…..

• Line 281:

Before: …Furthermore, with the scheme proposed in this paper,…

After: …Additionally, with the scheme proposed in this paper,…

 

Point 2: Most figures (ex, Fig. 3 (a) and (b), Fig. 4 (a) and (b)) are still hard to be distinguished for black and white prints.

 

Response 2:

Thanks for your very constructive comments. We have modified the figures and make them clear in black and white prints. We have listed the figures in black and white version as follow:

Point 3: In every equation, there is no comma(,) or a period (.). Further, it is wrong that "Where" after the expression where the capital letter begins.

 

Response 3:

Thanks for your constructive comments.

We have added a period after each equation. All the ‘Where’ after the expression have been revised.

• Line 89:

Before: Where SNR is measured by the uniform power training sequence…..

After: The SNR is measured by the uniform power training sequence….

• Line 95:

Before: Where  is the shaping factor of the PS signal.…..

After: The  is the shaping factor of the PS signal.….

• Line 102:

Before: Where  are the transmitting bits of the k_th symbol.…..

After: The  are the transmitting bits of the k_th symbol.….

• Line 105

Before: Where  and  represent for the subsets in  whose i_th bit is 1 or 0..…..

After: The  and  represent for the subsets in  whose i_th bit is 1 or 0..….

Author Response File: Author Response.docx