Encoding Efficiency Bounds for Digital Number Representations Under Value Deviation Constraints

When logic upsets affect machine words representing variables in programs, it is possible to consider their effect in terms of the numeric magnitude of the value deviation they induce. This is a result of the semantic interpretation that the bit-level layout of different language data types imposes. When some distribution of value deviations in variables may be acceptable, it is possible to consider techniques for encoding the representation of program variables, to limit the deviations of values in the presence of logic upsets, to acceptable distributions thereof. To quantify the best-case performance of encoding techniques for minimizing such value deviations, we investigate bounds for their encoding efficiency.