## 3 Joint Huffman and LDPC Coding Enabled Free-Space Optical Communication
### Results and Analysis  
The signal-to-crosstalk ratio (SCTR) gains achieved by SO are presented in Figure 5. The SCTR is measured after the OAM mode detection. It is defined as the power ratio of the desirable OAM mode and neighboring OAM modes, in the scenario where the desired OAM mode is generated exclusively at the transmitter. The insets in Figure 5(a1,a2) show the measured SCTR gains. The SCTR improvement of \(>\)1.6 dB is achieved for OAM state 2; and the SCTR gain of \(>\)1 dB is available for OAM state \(-6\). The data shows that the best SO is at 6 mm and 5 mm for OAM states 2, and \(-6\), respectively. For simplicity, the SO will be set to 5 mm for all following cases in this paper.  
In Figure 6, we analyze the effects of the nonuniform signaling. The data represents BER performance in the atmospheric turbulence-free environment. Figure 6a,b shows that the pre-FEC performance of 5-QAM is worse than that of the QPSK due to the implementation and DSP penalties. These data also indicate that the pre-FEC performance of 9-QAM can outperform the 8-QAM. However, the post-FEC OSNR penalties between the 5-QAM and QPSK are measured to be \(<\)0.3 dB and 0.2 dB, in the respective OAM states 2 and \(-6\), when the BER is \(10^{-4}\). In addition,  
Figure 4: Experimental setup for the joint Huffman and LDPC coding enabled FSO communication system. Insets: (**a1**) Huffman tree for 5-size alphabet; (**a2**) 5-QAM format with bit labeling; (**b1**) Huffman tree for 9-size alphabet; (**b2**) 9-QAM format with bit labeling.  
Figure 5: Signal-to-crosstalk ratio (SCTR) improvements obtained by the spatial offset (SO). Insets: The examples of SCTR calculation for (**a1**) OAM state \(-6\), and (**a2**) OAM state 2.  
9-QAM shows a better performance over GF(2) LDPC coded 8-QAM by 2.7 dB and 3.2 dB in respective OAM states 2 and \(-6\), when BER is \(10^{-4}\).  
The BER performance affected by atmospheric turbulence is shown in Figure 7. The data indicate that the pre-FEC BER performance gap between QPSK and 5-QAM shrinks in an atmospheric turbulence limited environment; while the pre-FEC BER performance of 9-QAM is better than that that of the 8-QAM. Figure 7a shows that, if OAM state 2 is under testing, the average OSNR gains of \(>\)1.6 dB and 5.6 dB are reached by 5-QAM and 9-QAM, respectively, when the post-FEC BER is \(10^{-4}\), compare to coded QPSK and 8-QAM. In addition, if OAM state \(-6\) is detected, as depicted in Figure 7b, the coding gains of \(>\)1.1 dB and 5.4 dB can be obtained when the post-FEC BER is \(10^{-4}\) respectively by comparing 5-QAM with QPSK, and 9-QAM with 8-QAM. It is noteworthy that we only measure the performances of OAM states 2 and \(-6\), this is due to the symmetry between OAM modes with positive and negative states. In other words, OAM state 2 will have a very similar performance as OAM state \(-6\).  
In order to clarify the performance improvements achieved by the coded modulation, the average OSNR requirements at BER \(=10^{-4}\) for 4/5/8/9-QAM formats are shown in Table 1. These data are  
Figure 6: BER vs. OSNR performance in the atmospheric turbulence-free environment, when (**a**) OAM state 2 is under testing; (**b**) OAM state \(-6\) is under testing.  
Figure 7: BER vs. average OSNR under an atmospheric turbulence limited environment, when (**a**) OAM state 2 is under testing; (**b**) OAM state \(-6\) is under testing.  
under conditions where OAM states 2 and 6 are detected, and with/without atmospheric turbulence. The OSNR penalties brought by atmospheric turbulence for OAM state 2, are concluded as 3.3 dB, 1.4 dB, 5.7 dB, and 2.8 dB for 4/5/8/9-QAM, respectively. Similarly, the mode-crosstalk penalties for OAM state \(-6\), are measured to be 3.1 dB, 1.8 dB, 5 dB, and 2.8 dB for 4/5/8/9-QAM, respectively. Thereafter, the nonuniform 5/9-QAM schemes have a higher inter-mode crosstalk tolerance over uniform QPSK and 8-QAM.