## 4 Experimental Results
### Experiments on 5.1 Channel and Stereo Audio  
Multichannel audio systems have become more and more popular in home entertainment environments. As HE-AAC is one of the most efficient audio codecs for multichannel audio, here we present experimental results under HE-AAC v1 and v2 compression by applying our watermarking algorithm on 5.1 channel audio and stereo audio, respectively. The CSNR for 5.1 channel audio was applied toHE-AAC v1 128 kbps compression, and, for stereo audio, it was applied to HE-AAC v2 48 kbps compression. We used the twelve 5.1 channel audio types, which are listed in Table 7. All 5.1 channel audio files were in WAVE format, sampled at 48 kHz, quantized with 16 bits, and 10-20 s long. Figure 13 shows the time domain waveforms of the \"Bach organ\" 5.1 channel audio. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{3}{*}{**Reference**} & \multirow{3}{*}{ \begin{tabular}{c} **Data** \\ **Payload** \\ **(bps)** \\ \end{tabular}  } & \multirow{3}{*}{**ODG**} & \multicolumn{3}{c}{**MP3 Compression BER (\%)**} & \multicolumn{3}{c}{**HE-AAC v1 Compression BER (\%)**} \\ \cline{3-11}  & & & **32** & **64** & **96** & **128** & **16** & **24** & **32** & **64** \\ \cline{2-11}  & & & **kbps** & **kbps** & **kbps** & **kbps** & **kbps** & **kbps** & **kbps** & **kbps** \\ \hline
[23] & 43 & \(-\)0.57 & 3.00 & 0.00 & 0.00 & 0.00 & — & — & — & — \\
[8] & 43 & \(-\)0.55 & — & 0.22 & 0.02 & — & — & — & — & — \\
[9] & 84 & \(-\)0.70 & — & — & 0.33 & 0.00 & — & — & — & — \\
[12] & 172 & \(-\)1.05 & 6.13 &The channels from, top to bottom, are front left (FL), front right (FR), center (C), low-frequency effects (LFE), surround left (SL), and surround right (SR). We independently embedded a watermark on each channel except LFE, as the channel showed nearly no signals in our test audio. Table 8 provides the BER of each channel of 5.1 channel audio under HE-AAC v1 128 kbps compression, as well as the corresponding ODG of each audio. The ODG was first calculated for each channel except LFE and averaged to report in the table for each audio. From the table, we can observe that there was a big difference of the BER of each channel of an audio. For example, the BER of the center channel of the No.1 audio was only 0.18%, but its front right channel BER was 5% higher than center channel, which was 6.21%. Regarding the ODG, all test audio yielded larger than \(-1\) ODG values, except for three test audios that were slightly lower than \(-1\). The average BER of the twelve test audios was 2.53%, and the average ODG was \(-0.84\). For testing stereo audio, we down-mixed the 5.1 channel audio by the following formula, FL = FL + 0.707 \(\times\) FC + 0.5 \(\times\) SL; FR = FR + 0.707 \(\times\) FC + 0.5 \(\times\) SR, to make test stereo audio. Figure 14 shows the time domain waveforms of the \"Bach organ\" stereo audio, which was made by the corresponding 5.1 channel audio. For the experiment on 5.1 channel audio, we independently embedded a watermark on each channel. Table 9 provides the BER of each channel of stereo audio under HE-AAC v2 48 kbps compression, as well as the corresponding ODG of each audio type. From the table, we can see that average BER of the twelve test audios was 1.28%, and the average ODG was \(-0.78\).