Correction to "Secure Integrated Sensing and Communication against Communication and Sensing Eavesdropping"

There is a small correction to the arxiv version of the paper. Since it only concerns typo I did not wish to upload a newer version.

The typo is in the bounded difference of martingale in (23) where the correct quantity should be

\[\phi_{s,s'} = \underset{x,y}{\max}\,\left|\log \frac{W_{Y_1|X,s}(y|x)}{W_{Y_1|X,s'}(y|x)}-\mathbb{D}(W_{Y_1|X,s}(\cdot|x)||W_{Y_1|X,s'}(\cdot|x))\right|\]

instead of conditional version as stated. Similarly following that

\(\mathbb{E}\left[L^{(1)}_{s,s';t}|\mathcal{F}_{t-1}\right] = \mathbb{D}(W_{Y_1|X,s}(\cdot|x_t)||W_{Y_1|X,s'}(\cdot|x_t))\) is the corrected statement. This has no bearing on the result of lemma 3 since the sum of per-symbol divergence over a completed constant-composition data segment (after initial estimation and barring the universal code during code structure transmission) equals to

\[(1-\Delta)(n-N-T)\mathbb{D}(W_{Y_1|X,s}||W_{Y_1|X,s'}|P_{X,s})\]