Data compression under constraints of causality and variable finite memory

Data compression techniques mainly consist of two operations, data compression itself and a consequent data de-compression. In real time, the compressor and de-compressor are causal and, at a given time, may process (or ‘remember’) only a fragment of the input signal. In the latter case, we say that such a filter has a finite memory. We study a new technique for optimal real-time data compression. Our approach is based on a specific formulation of two related problems so that one problem is stated for data compression and another one for data de-compression. A compressor and de-compressor satisfying conditions of causality and memory are represented by matrices with special forms, A and B, respectively. A technique for the solution of the problems is developed on the basis of a reduction of minimization problems, in terms of matrices A and B, to problems in terms of specific blocks of A and B. The solutions represent data compressor and data de-compressor in terms of blocks of those matrices that minimize associated error criteria. The analysis of the associated errors is also provided.