a random variable. Obviously, the uncertainty in $Y$ would be a measure of the average description length of the threshold/feedback.

Let ${\mathsf C}: [0,1] \times [0,1] \rightarrow [0,1]$ be a code (an allocation), which assigns for every 2-tuple $(Y_{N-1},Y_N)$ an element $Y := {\mathsf C}(Y_{N-1},Y_N) \in [0,1]$, such that $Y_{N-1} \leq Y < Y_N$. Let $Y$ have a discrete distribution, i.e., let there exist a set $\Omega_Y = \{y_1, y_2, \cdots \}$ and a set of probabilities $\{p_{y_1}, p_{y_2}, \cdots\}$ such that $\sum_{i=1} p_{y_i} = 1$, and $p_{y_i} := {\mathsf Pr}(Y = y_i)$. Then, the entropy of the random variable $Y$ (equivalently, the code ${\mathsf C}$) is defined as $$- \sum_{i=1}^{\infty} p_{y_i} \log_2(p_{y_i})$$ Clearly, the entropy would approximate the average length of the feedback required for a contention resolution algorithm that resolves a two tuple $(Y_{N-1},Y_N)$ with threshold ${\mathsf C}(Y_{N-1},Y_N)$.

The code ${\mathsf C}(,)$ can, in general, take a continuous sample space, all of $[0,1]$ and a useful description of entropy may not be possible in such cases. For continuous distribution $F(\cdot)$, ${\mathsf Pr}(Y_{N-1} \neq Y_N) = 1$, and for every $(Y_{N-1}, Y_N)$ such that $Y_{N-1} \neq Y_N$, there is some rational $Q$ such that $Y_{N-1} \leq Q < Y_N$. 