Optimal bit allocation with side information

For a given set of quantizers and a data vector, the optimal bit allocation in a rate/distortion sense is the sequence of quantizers which minimizes the overall distortion for a given bit budget. In an operational framework, this sequence is dependent on the data realization rather than on its probabilistic model and the cost of describing the sequence itself becomes therefore part of the bit budget. We present an allocation algorithm based on dynamic programming which determines the optimal bit allocation taking into account the side information of describing the structure of the allocation itself; practical simplifications of the algorithm are also presented with respect to coding of continuous data sources.