Abstract-The entropy of a set of data is a measure of the amount of information contained in it. Entropy calculations for fully specified data have been used to get a theoretical bound on how much that data can be compressed. This paper extends the concept of entropy for incompletely specified test data (i.e., that has unspecified or don't care bits) and explores the use of entropy to show how bounds on the maximum amount of compression for a particular symbol partitioning can be calculated. The impact of different ways of partitioning the test data into symbols on entropy is studied. For a class of partitions that use fixed-length symbols, a greedy algorithm for specifying the don't cares to reduce entropy is described. It is shown to be equivalent to the minimum entropy set cover problem and thus is within an additive constant error with respect to the minimum entropy possible among all ways of specifying the don't cares. A polynomial time algorithm that can be used to approximate the calculation of entropy is described. Different test data compression techniques proposed in the literature are analyzed with respect to the entropy bounds. The limitations and advantages of certain types of test data encoding strategies are studied using entropy theory.Index Terms-Entropy theory, linear feedback shift register (LFSR) reseeding, test data compression.

A new test access mechanism (TAM) for multiple identical embedded cores is proposed. It exploits the identical nature of the cores and modular pipelined circuitry to provide scalable and flexible capabilities to make tradeoffs between test time and diagnosis over the manufacturing maturity cycle from low-yield initial production to high-yield, high-volume production. The test throughput gains of various configurations of this TAM are analyzed. Forward and reverse protocol translations for core patterns applied with this TAM are described.

Abstract-The output space of a linear decompressor must be sufficiently large to contain all the test cubes in the test set. The ideas proposed in this paper transform the output space of a linear decompressor so as to reduce the number of inputs required thereby increasing compression while still keeping all the test cubes in the output space. Scan inversion is used to invert a subset of the scan cells while reconfiguration modifies the linear decompressor. Any existing method for designing a linear decompressor (either combinational or sequential) can be used first to obtain the best linear decompressor that it can. Using that linear decompressor as a starting point, the proposed methods improve the compression further. The key property of scan inversion is that it is a linear transformation of the output space and, thus, the output space remains a linear subspace spanned by a Boolean matrix. Using this property, a systematic procedure based on linear algebra is described for selecting the set of inverting scan cells to maximize compression. A symbolic Gaussian elimination method to solve a constrained Boolean matrix is proposed and utilized for reconfiguring the linear decompressor. The proposed schemes can be utilized in various design flow scenarios and require no or very little hardware overhead. Experiments indicate that significant improvements in compression can be achieved.Index Terms-Linear decompression, linear feedback shift register (LFSR) reseeding, on-chip decompression, test data compression, XOR network.

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