On the Performance of Resilient Functions with Imperfect Inputs

We analyze the performance of resilient functions for imperfect input bits. Specifically, we allow more input bits than the resiliency degree of the resilient function to be biased and analyze the output behavior under this new assumption. We develop bounds on the output distribution of resilient functions build from a number of families of linear codes. We develop an explicit formula for the probability of producing an imperfect output bit that works halfway beyond the resiliency degree. It turns out that this probability shrinks exponentially with increasing code length. We provide strong evidence that suggests that resilient functions build from linear codes performs close to perfect half-way beyond their designed resiliency degree. Index Words – Resilient functions, extractors, min-entropy.