## 3 Biomimetic Covert Whistle Transmitter  
For a low BER, the conventional digital communication utilizes the forward error correction (FEC) method. The FEC provides a connection rule to concatenated additional symbols and corrects the erroneous bits, but requires the additional bits that reduce the data rate [23; 24]. In cases of small bandwidth UWA communication systems, the data rate is one of the important parameters. Thus, the proposed biomimetic communication scheme is developed to obtain a low BER and large DoM, without sacrificing the data rate. The proposed method reclassifies the real whistles into a large number of subgroups to have larger distances among subgroups and provide link information among subgroups to utilize all subgroups. The detailed procedure and an example are described in this section. Assume that the maximum number of groups for the optimum accuracy is given as \(K_{\text{opt}}\), and the maximum number of bits per whistle is given as \(M_{\text{opt}}=\left\lfloor\log_{2}K_{\text{opt}}\right\rfloor\), and \(K_{\text{opt}}\) may not be the same as \(2^{M_{\text{opt}}}\). To increase the BER performance and preserve the same data rate, the proposed method reclassifies the \(K_{\text{opt}}\) groups into enlarged subgroups \(K_{\text{tot}}=(2^{a}\times K_{\text{opt}})\), and generates many subgroup sets, in which one subgroup set consists of \(2^{M_{\text{opt}}}\) subgroups among \(K_{\text{tot}}\) subgroups. The possible number of the subgroup sets with the size of \(2^{M_{\text{opt}}}\) is very large, but in this paper, \(K_{\text{tot}}\) subgroup sets that have large distances are chosen. If we carefully select the subgroup sets whose distances are larger than those of the first classified \(K_{\text{opt}}\) group sets, we attain a lower error rate performance. The proposed link information that connects all subgroup sets is determined by the link matrix (\(H\)) with the size of \(K_{\text{tot}}\times 2^{M_{\text{opt}}}\) that one row consists of the one subgroup set with a size of \(2^{M_{\text{opt}}}\) and the total number of rows is \(K_{\text{tot}}\). The \(i\)-th column index is mapped to input bits for the binary allocation, e.g., binary counter or Gray code, and every element value of \(H\) indicates the current subgroup and the row number for the next input bits. Then, the link information between two subgroup sets is established. In order to avoid falling into a short loop by the subgroup loop indexing, the element value of a row of \(H\) is not allowed to include the same row index and the elements of the one subgroup set is not the same as that of other subgroup sets, and all indices occur evenly \(2^{M_{\text{opt}}}\) times. This additional link information helps the receiver to decode the distorted received symbols and attain a better BER performance. A link matrix \(H\) is given as below,  
\[H=\left[ \begin{array}{ccccc}h_{1,1}&\cdots&h_{1,i}&\cdots&h_{1,2^{M_{\text{ opt}}}}\\ &&\vdots&&\\ h_{k,1}&\cdots&h_{k,i}&\cdots&h_{k,2^{M_{\text{opt}}}}\\ &&\vdots&&\\ h_{K_{\text{tot}},1}&\cdots&h_{K_{\text{tot}},i}&\cdots&h_{K_{\text{tot}},2^{M_ {\text{opt}}}}\end{array} \right] \tag{3}\]Assume that a \(N\) bit stream is represented as the vector of \(\mathbf{B}=\{b_{1},\cdots,b_{n},\cdots,b_{N}\}\), where the size of \(b_{n}\) is equal to \(M_{\text{opt}}\). When \(b_{1}\) is input, the \(b_{1}\) binary value is translated to a decimal number which is the index of the column of the first row. The selected element of the first row indicates the subgroup index for \(b_{1}\), and a whistle in the indicated subgroup is randomly chosen and transmitted. Subsequently, the element selected by \(b_{1}\) also provides the row number of \(H\) for the next input \(b_{2}\). For \(b_{2}\), the same procedure is performed for the input \(b_{1}\). This procedure is executed to all elements of \(\mathbf{B}\). If the size of \(\mathbf{B}\) is large, all elements of \(H\) will be picked and all whistles will be utilized for the transmission, which preserves the large DoM.