In our previous works, we defined Local Information Privacy (LIP) as a context-aware privacy notion and presented the corresponding privacy-preserving mechanism. Then we claim that the mechanism satisfies epsilon-LIP for any epsilon>0 for arbitrary Px. However, this claim is not completely correct. In this document, we provide a correction to the valid range of privacy parameters of our previously proposed LIP mechanism. Further, we propose efficient algorithms to expand the range of valid privacy parameters. Finally, we discuss the impact of updated results on our original paper's experiments, the rationale of the proposed correction and corrected results.

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