Compression and Filtering of Random Signals Under Constraint of Variable Memory

The authors study a new technique for optimal data compression subject to conditions of causality and different types of memory. The technique is based on the assumption that some information about compressed data can be obtained from a solution of the associated problem without constraints of causality and memory. This allows one to consider two separate problem related to compression and decompression subject to those constraints. Their solutions are given and the analysis of the associated errors is provided.