= y_{min}$ $y_{min} = y_{min} + (y_{max} - y_{min}) \times (1 - \frac{1}{3})$ $y_{max} = y_{min}$ $y_{min} = y_{min} + (y_{max} - y_{low}) \times (1 - \frac{1}{3})$ $k = k + 1$ ($f \neq 1$)

Using simulations, we observe that the average effort needed to resolve contention is $1.89$ slots much less than the $2.12$ slots required by OSA. The proposed algorithm makes use of the fact that, in the event of a collision, the probability that two users are involved is significantly higher than the probability that three users are involved in the collision. The contention resolution problem was formulated as identifying a random threshold $Y$ between $Y_1$ and $Y_2$ ($Y_1 < Y \leq Y_2$) or between $Y_2$ and $Y_3$ ($Y_2 \leq Y < Y_3$). The entropy of the proposed strategy was observed to be strictly smaller than the entropy of the maximal probability allocation scheme of OSA.

Correlated Channel
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We consider a wireless downlink channel with $N = 2$ users. We assume that the wireless channel of the two users is correlated with the sample space, $\Omega_H = \{ (4,2), (4,6), (8,6), (8,10), (12,10), (12,14), (16,14)\}$ and with the joint probabilities $p_{H} = \{ \frac{1}{7} - 6 