efficiency can be adapted by the and the code rate $R_\mathsf{c}$, and a single code can be used. Note that every eigenvalue is protected by the code as is performed after the and decoding and demapping can be performed independently. Thus, shares these advantages with .

We wish for a high code rate $R_\mathsf{c}$ to keep the performance degradation due to the time-sharing low. More precisely, we wish to maximize the number of symbols distributed according to $p_X^*(\lambda)$. The ratio between information symbols and coded symbols, denoted by $R_\mathsf{ts}$, is an indication for the expected performance degradation, $$\begin{aligned}
R_\mathsf{ts} &= \frac{\frac{n_\mathsf{c} R_\mathsf{c}}{\log_2(M)}}{\frac{n_\mathsf{c}R_\mathsf{c}}{\log_2(M)} + \frac{n_\mathsf{c}(1-R_\mathsf{c})}{\log_2(M_\mathsf{par})}}\nonumber\\
&= \frac{R_\mathsf{c}\log_2(M_\mathsf{par})}{\log_2(M)(1-R_\mathsf{c})+R_\mathsf{c}\log_2(M_\mathsf{par})}.
\label{eqn:shaping:R_ts}\end{aligned}$$

Parity symbols
--------------

The parity symbols at the output of the code encoder are uniformly distributed. In [Fig.]{}, we observed that with uniform signaling, i.e., $\Lambda_\mathsf{par}=\{\lambda_1, \lambda_M\}$ and $M_\mathsf{par}=2$, is optimal for low as it achieves capacity and performs reasonably well for high . However, we note from [Fig.]{} that for a higher order modulation, even with uniform signaling, higher rates are possible. Hence, here we consider a scenario where $M_\mathsf{par}>2$. We further increase the rate by only using a subset of $\Lambda$ and by picking the eigenvalues such that they are not 