variable. We illustrate our formulation by studying the opportunistic splitting algorithm [@qin-berry-osa]. We show that OSA is a maximal probability allocation scheme and we conjecture that MPA is an entropy minimizing strategy and a delay minimizing strategy as well. In this work, we have studied opportunistic scheduling for $N$ users with i.i.d. channel gains. We believe that our formulation of contention resolution as a source code can help develop optimal strategies for a variety of other network scenarios as well.

Related Literature
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The idea of splitting with ternary feedback was originally proposed for scheduling users in Aloha type networks (see [@gallager-conflictresolution]). In [@arrow-etal-binaryquestions], Arrow et al., study a problem of resolving the user with the highest sample value with binary type questions. The optimal strategy was studied when accurate feedback of the number of contending users involved in every slot was available. The near optimality of greedy strategies (like MPA studied in Section \[sec:osa\_source\_coding\]) was also discussed in [@arrow-etal-binaryquestions]. In [@anantharam-varaiya-conflictresolution], Anantharam and Varaiya prove the optimality of binary type questions to minimize the average delay in [@arrow-etal-binaryquestions]. The performance of binary type questions in the presence of ternary feedback was first reported in [@cohen-etal-ternaryfeedback]. The optimal thresholds were 