## 3 System Model
### PPI Interleaver Mechanism  
As per the PPI method [26], shown in Figure 3, two mother interleavers K\({}_{1}\) and K\({}_{2}\) have been assigned to the first two users. The interleaving pattern for the third user is generated by interleaving the pattern of K\({}_{2}\) with the pattern of K\({}_{1}\), and the fourth user is assigned the pattern after interleaving the pattern of K\({}_{3}\) with the pattern of K\({}_{2}\). In sequence to this, to generate the patterns for the fifth and sixth users, patterns K\({}_{3}\) and K\({}_{4}\) work as mother interleavers. User K\({}_{5}\) has been assigned the interleaving pattern after interleaving the pattern of K\({}_{4}\) with the pattern of K\({}_{3}\), and user K\({}_{6}\) has been assigned the interleaving pattern after interleaving the pattern of K\({}_{5}\) with the pattern of K\({}_{4}\). Therefore, in this method, starting with two mother interleavers, successive interleaving patterns are generated, and the mother interleaving pattern changes continuously. This results in a relatively secure system in comparison to the power interleaver (PI) [39] suggested in the literature. Figure 3: PPI interleaver generation. Sequence of PPI pattern generation at different stages in a communication system:  
* Sequence of base station interleaving pattern generation  
First user is assigned with interleaving pattern \(\mathrm{K_{1}}\) and second user is assigned with interleaving pattern \(\mathrm{K_{2}}\). The third user is assigned with interleaving pattern \(\mathrm{K_{3}}\equiv\mathrm{K_{1}}(\mathrm{K_{2}})\), i.e., interleaving \(\mathrm{K_{2}}\) pattern with the pattern of \(\mathrm{K_{1}}\). The fourth user is given interleaving pattern \(\mathrm{K_{4}}\equiv\mathrm{K_{2}}(\mathrm{K_{3}})\), i.e., interleaving \(\mathrm{K_{3}}\) pattern with the pattern of \(\mathrm{K_{2}}\), and so on for the following users. The first user is assigned interleaving pattern \(\mathrm{K_{1}}\), and the second user is assigned interleaving pattern \(\mathrm{K_{2}}\). The third user is allocated interleaving pattern \(\mathrm{K_{3}}\), which is equivalent to interleaving pattern \(\mathrm{K_{2}}\) with the pattern of \(\mathrm{K_{1}}\). Similarly, the fourth user is assigned interleaving pattern \(\mathrm{K_{4}}\), equivalent to interleaving pattern \(\mathrm{K_{3}}\) with the pattern of \(\mathrm{K_{2}}\), and so forth for subsequent users. * Sequence of mobile station interleaving pattern generation  
Provided that for each value of \(\mathrm{n}\geq 1\), interleaving patterns are transmitted for all \(\mathrm{2n}-1\) and \(\mathrm{2n}\) users, input the user number \(\mathrm{k}\) and figure out '\(\mathrm{n}\)' such that \(\mathrm{2n}<\mathrm{k}<\mathrm{2n}+1\). Following the above-mentioned algorithm at most \(\mathrm{2n}-1\) interleaving cycles are needed to generate interleaving pattern for the possible largest value of \(\mathrm{k}\). At the mobile station, the interleaving pattern for each user is determined based on the user number assigned by the base station, minimizing the need for extensive information exchange. Additionally, a set of intermediate interleaving patterns is transmitted alongside primary interleavers to simplify computational tasks at the mobile station. This approach reduces the number of required interleaving cycles, especially when the base station broadcasts interleaving pattern generation methods for \(\mathrm{2^{n}-1}\) and \(\mathrm{2^{n}}\) users across all applicable values of \(\mathrm{n}\geq 1\). For example, when considering a user \(\mathrm{k}=31\), the calculation indicates that \(\mathrm{n}\) equals 4, thus if interleaving patterns for (\(\mathrm{2^{n}-1}\)) and \(\mathrm{2^{n}}\) users (15 and 16) are available, a maximum of \(\mathrm{2^{n}-1}\) (15) additional cycles are required to compute the interleaving pattern for the 31 st user. * Interleaving pattern generation during the implementation of MUD  
The next user pattern generation depends upon the previous two user's patterns and needs a single cycle only.