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arXiv · 2507.11452

On the paper Optimal dual frames of probabilistic erasures

Shankhadeep Mondal·Ram Narayan Mohapatra
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Abstract

In the paper Optimal Dual Frames for Probabilistic Erasures, the authors have given conditions under which the canonical dual is claimed to be the unique probability optimal dual for 1-erasure reconstruction. In this paper, we demonstrate via counterexamples that the conditions provided are not sufficient to guarantee uniqueness. We also noticed a mistake in the proof of the theorem and proved the correct version of the theorem with a stronger but valid condition. Furthermore, we show that the corollary asserting uniqueness for a tight frame assumption is also incorrect. Our results refine the understanding of probability optimal dual frame constructions and offer a more complete characterization of the 1-erasure probability optimal duals.

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Shankhadeep Mondal, Ram Narayan Mohapatra. 2025-07-15. On the paper Optimal dual frames of probabilistic erasures. https://arxiv.org/abs/2507.11452

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