SIC Error Towards the Packet Error Rate: Optimal Partitioning in OTFS-NOMA Systems

\textit{A system including a lamp and a door, each of which has two possible states $1$ or $0$, i.e., ''on/open'' and ''off/closed'': the states of the door and the lamp are independent of each other and the total Markov chain is the one with memory of variable length with the context-tree $(\tau, \mathscr{p})$ with regard to the transition probability $\mathscr{p}$ and $\tau\stackrel{def}{=}\{1, 10, 100, \cdots\}\cup \{ 0^{\infty}  \}$. Now, consider the lamp and the total system as the successive interference cancellation (SIC) error $-$ due to the imperfect SIC $-$ and the total packet error rate, respectively. How can we optimally determine the aforementioned variable length and adjust its variability in practice?} This paper technically explores orthogonal time-frequency-space (OTFS) modulation assisted non-orthogonal multiple access (NOMA) systems and the packet error rate mainly arising from the SIC imperfectness from an information-theoretic point of view. With a given prior distribution, we aim at marginalising over $\mathscr{SUFF}$ on all models $\mathscr{SUFF}$ of maximal depth $\mathscr{D}$ where according to the nature of the OTFS-NOMA principle, $\Big(\mathscr{SUFF}, \mathscr{D} \Big)=f\Big(\mathcal{T} (sec), \Delta f (Hz), \mathcal{N}^{(sample)}, \mathcal{M}^{(sample)}\Big)$ holds as a function of the OTFS-NOMA pair $\Big(\mathcal{N}^{(sample)}, \mathcal{M}^{(sample)}\Big)$. We theoretically make a solution to two scenarios of the availability and unavailability of the casual state-information (CSI) at the encoder, as well as an interpretation over e.g. enegy-level.