Relating entropy theory to test data compression

The entropy of a set of data is related to the amount of information that it contains and provides a theoretical bound on the amount of compression that can be achieved. While calculating entropy is well understood for fully specified data, this paper explores the use of entropy for incompletely specified test data and shows how theoretical bounds on the maximum amount of test data compression can be calculated. An algorithm for specifying don't cares to minimize entropy for fixed length symbols is presented, and it is proven to provide the lowest entropy among all ways of specifying the don't cares. The impact of different ways of partitioning the test data into symbols on entropy is studied. Different test data compression techniques are analyzed with respect to their entropy bounds. Entropy theory is used to show the limitations and advantages of certain types of test data encoding strategies.