diagram of the -based system.[]{data-label="fig:system:block_diagram_nft"}](block_diagram_nft)

As in [@shevchenko2018tcom], we embed information in the imaginary part of the discrete spectrum, also referred to as eigenvalues. Hence, the input of the channel is an $X\in\Lambda=\{\lambda_1,\ldots,\lambda_M\}$, where $\Lambda$ is the set of eigenvalues, $\lambda_i$ is the $i$th eigenvalue, and $M$ is the order of the modulation. The eigenvalues $\{\lambda_i\}$ are assumed to be ordered in ascending order by their imaginary parts. Furthermore, the output of the channel is an $Y\in\Psi$, where $\Psi = \{y\in\mathbb{C}: {\mathfrak{R}\{y\}}=0, {\mathfrak{I}\{y\}}\geq 0\}$. A block diagram is depicted in [Fig.]{}. The information embedded in a single eigenvalue $\lambda\in\Lambda$ is transformed to a time-domain signal $q(t,0)$ via the where the transmitter is located at position $z=0$ along the fiber. At position $z=1$, the receiver calculates the discrete spectrum $\psi\in\Psi$ from the received signal $q(t,1)$ via the . The time-domain signal corresponds to first order solitons, i.e., $$\begin{aligned}
    q(t,0) &= 2{\mathfrak{I}\{\lambda\}} {\operatorname{sech}{\mathopen{}\mathclose\bgroup\originalleft}(2{\mathfrak{I}\{\lambda\}} t{\aftergroup\egroup\originalright})}.\end{aligned}$$ For the to be valid, the signal must have finite support, i.e., before transmitting the next pulse, the previous one must have returned to zero. As the pulses in general have infinite tails, we truncate them when they fall below a threshold close to zero. We define the 