In Remark \[rem:osa\_2\], for the $N = 2$ case, we noticed that the feedback from the base station corresponding to a threshold can be viewed as the binary representation of the threshold itself. For general $N$, the feedback from the base station can still be viewed as the binary representation of the threshold, however, with the weights corresponding to a position computed from the thresholds $\{ y_k \}$ obtained from the pseudo-code. For example, the weight of the first position will be equal to $y_1$.

![Plot of the average delay performance of OSA and MPA as a function of the number of users $N$. We have also plotted the entropy of the threshold random variable corresponding to MPA.[]{data-label="fig:osa_vs_mpa"}](osa_vs_mpa.pdf)

In Figure \[fig:osa\_vs\_mpa\], we plot the average delay performance of OSA (as described in Section \[sec:osa\]) and the maximal probability allocation code. As expected, the performance of OSA and MPA are similar and in fact, MPA performs better than OSA as it identifies the optimal thresholds without any approximations (see Remark \[rem:osa\]). We have also plotted in the Figure \[fig:osa\_vs\_mpa\], the entropy of the maximal probability allocation code in bits. As expected, the entropy of the random variable reflects the average delay 