We propose and study a variant of pliable index coding (PICOD) where receivers have preferences for their unknown messages and give each unknown message a preference ranking. We call this the preferential pliable index-coding (PPICOD) problem and study the Pareto trade-off between the code length and overall satisfaction metric among all receivers. We derive theoretical characteristics of the PPICOD problem in terms of interactions between achievable code length and satisfaction metric. We also conceptually characterise two methods for computation of the Pareto boundary of the set of all achievable code length-satisfaction pairs. As for a coding scheme, we extend the Greedy Cover Algorithm for PICOD by Brahma and Fragouli, 2015, to balance the number of satisfied receivers and average satisfaction metric in each iteration. We present numerical results which show the efficacy of our proposed algorithm in approaching the Pareto boundary, found via brute-force computation.

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