Optimal Reference Selection for Random Access in Predictive Coding Schemes

Data acquired over long periods of time like High Definition (HD) videos or records from a sensor over long time intervals, have to be efficiently compressed, to reduce their size. The compression has also to allow efficient access to random parts of the data upon request from the users. Efficient compression is usually achieved with prediction between data points at successive time instants. However, this creates dependencies between the compressed representations, which is contrary to the idea of random access. Prediction methods rely in particular on reference data points, used to predict other data points. The placement of these references balances compression efficiency and random access. Existing solutions to position the references use ad hoc methods. In this paper, we study this joint problem of compression efficiency and random access. We introduce the storage cost as a measure of the compression efficiency and the transmission cost for the random access ability. We express the reference placement problem that trades storage with transmission cost as an integer linear programming problem. Considering additional assumptions on the sources and coding methods reduces the complexity of the search space of the optimization problem. Moreover, we show that the classical periodic placement of the references is optimal, when the encoding costs of each data point are equal and when requests of successive data points are made. In this particular case, a closed-form expression of the optimal period is derived. Finally, the proposed optimal placement strategy is compared with an ad hoc method, where the references correspond to sources where the prediction does not help reducing significantly the encoding cost. The proposed optimal algorithm shows a bit saving of -20% with respect to the ad hoc method.