Bit Truncation Optimal Value Setting Considering Bit Failures

Bit truncation is one of the widely-applied techniques to enable quality-adaptive computing systems. In this paper, we take bit failures into consideration and give probabilistic analysis on bit truncation. Given the index set of truncated bits, we propose a data-driven approach to obtain the dummy value setting for the truncated bits such that the expected mean-squared error of data stream is minimized. Specifically, if the original binary data is evenly distributed, the approach can be greatly simplified. Our method works for any given truncation index set, instead of merely the traditional index set in which only continuous least-significant-bits are truncated. Numerical experiments on multimedia applications show that the proposed algorithm can greatly reduce the data noise and meanwhile save storage space, compared with the traditional all-zeros value setting method and the intuitive heuristic method.