Hence, we can always identify a code with a countable sample space for any continuous $F(\cdot)$ and define its entropy. Further, the feedback from the base station for any contention resolution algorithm is a finite sequence in ternary alphabet. Hence, we will always seek a code with a discrete distribution for $Y$. In such a framework, our objective could be to identify the code with the minimum entropy.

1.  The maximal probability allocation scheme of OSA (see Section \[sec:osa\_source\_coding\]) provides us a discrete distribution for the random threshold $Y$ with a finite entropy.

2.  The ternary description of the threshold does not use all the alphabets completely. For example, the alphabet $1$ appears only at the end of every code word (EoC). Further, the code is non-singular but need not be uniquely decodable as the codes are decoded one at a time. Hence, the entropy of the threshold need not exactly measure the average feedback length (and the average delay).

3.  We have assumed that the code ${\mathsf C}$ is a function only of the two tuple $(Y_{N-1}, Y_N)$. For correlated wireless channels and for arbitrary feedback schemes, we may need to consider ${\mathsf C}$ as a function of the 