case). An optimal choice of the thresholds can minimize the average description length of the feedback and the delay to resolve contention.

In Section \[sec:source\_coding\], we will propose a general framework for contention resolution for opportunistic scheduling motivated by the above observations.

A Source Coding Problem {#sec:source_coding}
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In this section, we will formulate contention resolution for opportunistic scheduling with ternary feedback as identifying a random threshold (channel gain) that separates the best channel from the other samples. Let $(X_1, X_2, \cdots, X_N)$ correspond to the vector of i.i.d. channel gain values in a slot and let $(Y_1, Y_2, \cdots, Y_N)$ be the ordered N-tuple of channel gain values of the $N$ users such that $0 \leq Y_1 \leq Y_2 \leq \cdots \leq Y_{N-1} \leq Y_N \leq 1$. The base station seeks to identify $\arg \max_{\{i=1,\cdots,N\}} \{ X_1, \cdots, X_N\}$, or, equivalently, $\arg \{Y_N\}$ in the slot. We aim to resolve the contention by identifying a threshold $Y$ such that $Y_{N-1} \leq Y < Y_N$; the base station will feedback the threshold $Y$ using ternary alphabet of $0,1$ and $e$ which aids in resolving the contention. $Y_{N-1}$ and $Y_N$ are random variables, and hence, the threshold $Y$ will also be 