Frequency-Directed Run-Length (FDR) Codes

Abstract

Test data compression and test resource partitioning (TRP) are necessary to reduce the volume of test data for system-on-a-chip designs. In the previous chapter, we showed that Golomb codes can be used for efficiently compressing SOC test data. In this chapter1, we present a new class of variable-to-variablelength compression codes that are designed using the distributions of the runs of Os in typical test sequences. We refer to these as frequency-directed run-length (FDR) codes. We present experimental results for ISCAS 89 benchmark circuits and an IBM production circuit to show that FDR codes outperform Golomb codes for test data compression. We also present a decompression architecture for TRP based on FDR codes, and an analytical characterization of the amount of compression that can be expected using these codes. Our analysis provides lower and upper bounds on the compression expected for some generic parameters of the test sequences. These bounds are especially tight when the number of runs is small, thereby showing that FDR codes are robust, i.e., they are insensitive to variations in the input data stream. In order to highlight the inherent superiority of FDR codes, we present a probabilistic analysis of data compression for a memoryless data source. Finally, we derive entropy bounds for the benchmark test sets and show that the compression obtained using FDR codes is quite close to the entropy bounds.