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This paper considers a single-input single-output broadcast channel with receiver side information. We find the optimal clique cover index code and the optimal transmission time allocation that minimize outage probability when total transmission time is limited. As our problem is NP-hard, we first find the optimal time allocation for a given index code. Then, we describe a brute-force algorithm that finds the set of all decodable index codes and chooses the optimal one adopting the optimal time allocation. To reduce the computational complexity of the brute-force algorithm, we propose a pruning algorithm which solves the same problem using the Hasse diagram but does not harm the optimality. Our analysis reveals that the optimal index code is dependent on the channel conditions, not simply on the number of required transmissions, which implies that the index coding-channel coupling improves the outage …