Concurrent error detection in 2-D separable linear transform
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As process technology continues to scale to smaller geometries and reduces the supply voltage, reliability of the resulting semiconductor becomes a greater concern. The effect of deep submicron noise, soft errors, variation, and aging degradation pose challenges on the functional correctness of VLSI systems and places roadblocks on reductions in scale. On the other side, as computing moves toward mobile, the energy efficiency of digital systems becomes one of the most important design metrics. However, reliability and energy efficiency are contradicting design requirements. Adding a voltage guard band is the most common method to mitigate the reliability impacts in such instances. Low power design technique like voltage over-scaling (VOS) even reduces the power by scaling the supply voltage just before data-dependant timing errors start to appear. Concurrent error detection is the solution to tackle reliability and energy-efficiency in a unified manner. Fault tolerance can be deployed at different design hierarchies. Given its low overhead, algorithm level error detection is an attractive approach. In this work, a generic weighted checksum code based error detection algorithm targeted generic 2-D separable linear transform is proposed. This technique encodes the input array at the 2-D linear trans- formation level, and algorithms are designed to operate on encoded data and produce encoded output data. The proposed error detection technique is a system-level method and therefore can be used in existing hardware or software 2-D linear transformation architectures with low overhead. The mathematic proof of the algorithm is provided within the scope of this dissertation. The checksum weighting vector for several common transforms are derived as examples, error detection cost and algorithm effectiveness are analyzed. In traditional fault tolerance study, the error is often evaluated at the boolean level. Many DSP applications, like 2-D linear transformation used in the multimedia compression system, do not require exactly correct results, but rather that the quality of the output is within the acceptable range. A generic quality aware error detection in the 2-D separable linear transform is proposed by extending the above property and defining the errors at the functional level. As an example, the quality-aware error detection technique is deployed on a low-power wavelet lifting transform architecture in JPEG2000. A low-cost Signal to Noise Ratio (SNR) aware detection logic based on proposed scheme is integrated into the discrete wavelet lifting transform architecture. This detection logic checks whether the image quality degradation caused by voltage over-scaling induced timing errors is acceptable and determines the optimal voltage set point in operating conditions at run time. This novel quality-based error detection approach is significantly different from traditional error detection schemes which look for exact data equivalence. A simulation result for one design shows that the supply voltage can be scaled down to 75% of the nominal voltage in typical process corner without significant image quality degradation, which translates to 9.15mW power consumption (44% power saving).