Failure mitigation in linear, sesquilinear and bijective operations on integer data streams via numerical entanglement

Abstract

A new roll-forward technique is proposed that recovers from any single fail-stop failure in $M$ integer data streams ($M\geq3$) when undergoing linear, sesquilinear or bijective (LSB) operations, such as: scaling, additions/subtractions, inner or outer vector products and permutations. In the proposed approach, the $M$ input integer data streams are linearly superimposed to form $M$ numerically entangled integer data streams that are stored in-place of the original inputs. A series of LSB operations can then be performed directly using these entangled data streams. The output results can be extracted from any $M-1$ entangled output streams by additions and arithmetic shifts, thereby guaranteeing robustness to a fail-stop failure in any single stream computation. Importantly, unlike other methods, the number of operations required for the entanglement, extraction and recovery of the results is linearly related to the number of the inputs and does not depend on the complexity of the performed LSB operations. We have validated our proposal in an Intel processor (Haswell architecture with AVX2 support) via convolution operations. Our analysis and experiments reveal that the proposed approach incurs only $1.8\%$ to $2.8\%$ reduction in processing throughput in comparison to the failure-intolerant approach. This overhead is 9 to 14 times smaller than that of the equivalent checksum-based method. Thus, our proposal can be used in distributed systems and unreliable processor hardware, or safety-critical applications, where robustness against fail-stop failures becomes a necessity.