## 2 Review of Low Frequency Ultrasonic Communication-based Audio Markers
### Audio Marker Transmitter  
The LFU communication-based audio marker transmitter sends an audio marker of a short text m in binary format though the LFU wave with three processing steps: FEC encoding, DPSK modulation, and gain normalization. First, the \(P\) binary bits to be transmitted at the \(i\)-th symbol are grouped as \(\mathbf{b}_{i}=\left[b_{i}^{1}\cdots b_{i}^{p}\cdots b_{i}^{p}\right]\), where \(P=24\) in this paper. Next, \(\mathbf{b}_{i}\) is then encoded by an FEC algorithm [19]; thus, additional error correction bits are attached. In particular, a perfect binary Golay code, \(G_{23}\), is used for FEC encoding [19], i.e., \(\mathbf{b}_{i}\) is reshaped into an \(O\times 12\) matrix, and it is encoded by the (23,12) Golay block. Consequently, an \(O\times 23\) encoded block for the \(i\)-th symbol, \(\mathbf{\widetilde{b}}_{i}\), is generated. Note here that \(O=2\) and the coding rate of \(G_{23}\), \(R_{c}=52.17\%\) in this paper.  
After FEC encoding, each encoded bit of \(\mathbf{\widetilde{b}}_{i}\) is modulated by DPSK. In other words, \(\mathbf{\widetilde{b}}_{i}\) is reshaped into a \(1\times 46\) vector, \(\mathbf{\widetilde{b}}_{i}=\left[\mathbf{\widetilde{b}}_{i}^{1}\cdots\mathbf{ \widetilde{b}}_{i}^{q}\cdots\mathbf{\widetilde{b}}_{i}^{p}\right]\), where \(Q=46\) in this paper. Then, differential encoding is applied to \(\mathbf{\widetilde{b}}_{i}^{j}\), as in [15]:  
\[d_{i}^{q}=\mathbf{\widetilde{b}}_{i}^{n}\
abla d_{i-1}^{q} \tag{1}\]  
where \(d_{i}^{q}\) is the \(q\)-th differentially encoded bit at the \(i\)-th symbol, and \(\
abla\) indicates the bitwise exclusive or (XOR) operation. After that, \(d_{i}^{q}\) is modulated with a sinusoidal signal by the windowed DPSK, so that:  
\[c_{i}(n+qT_{b})=w(n)\cos\!\left(\frac{2\pi f_{c}n}{f_{\mathrm{s}}}+\pi\!\left( 1-d_{i}^{q}\right)\right)\!,n=1,2,\cdots,T_{b} \tag{2}\]  
In Equation (2), \(T_{b}\) is the symbol length and is set to 96 because this is known as being the optimum by taking into account both the data transmission rate and communication robustness in noisy environments [15]. Moreover, \(f_{c}\) and \(f_{\mathrm{s}}\) are a carrier frequency and a sampling frequency of the modulated signal, respectively. Here, \(f_{\mathrm{s}}\) is set to 48 kHz to support the frequency range of most COTS microphones and speakers. Accordingly, \(f_{c}\) can be set from 18 to 20 kHz; it is set to 20 kHz in this paper. In addition, \(w(n)\) is a squared Hanning window, which can smooth the discontinuity between subsequent symbols to avoid unwanted impulsive noise in the modulated signals.  
Figure 2: Block diagram of a conventional low frequency ultrasound (LFU) communication-based audio marker system. DPSK: differential phase shift keying; FEC: forward error correction; BPF: bandpass filter.  
Next, the modulated signal in Equation (2), \(c_{i}(n+qT_{b})\), is subsequently normalized by its gain, so that:  
\[s_{i}^{T_{b}}(n+qT_{b})=\frac{Gc_{i}(n+qT_{b})}{\frac{1}{T_{b}}\sum_{n=1}^{T_{b}} \abs{c_{i}(n+qT_{b})}} \tag{3}\]  
where \(G=2^{14}\) is a normalization scale that corresponds to a half maximum sample value for a 16-bit resolution. Finally, the modulated LFU signal for the \(i\)-th symbol for all \(q\), \(s_{i}^{T_{b}}(n)\), is transformed into an analogue signal by a digital-to-analogue converter (DAC), and then it spreads through the aerial medium.