providing necessary feedback to aid in the resolution. We assume that a time slot comprises of $K$ mini slots, where the mini slots are used to resolve the contention. For example, the users can transmit MAC packets (like RTS/CTS in IEEE 802.11 DCF), possibly with some channel information, to the base station in a minislot and the base station can feed back the state of the contention in that slot. We assume that the base station feeds back the result of the contention within the minislot and the feedback of the base station is received by all the nodes in the network without any error. At the end of the contention process, the user that succeeded in the contention is permitted to transmit data in the remainder of the slot. In this setup, an objective of the base station would be to minimize the average number of minislots required to identify the user with the highest channel gain.

Opportunistic Splitting {#sec:osa}
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In this section, we briefly describe a contention resolution strategy, opportunistic splitting algorithm (OSA) from [@qin-berry-osa], for a fixed number of users $N$ and for i.i.d. block fading wireless channel. Polling for opportunistic scheduling requires $N$ minislots to 