Correction: Sensing-Assisted Secure Communications over Correlated Rayleigh Fading Channels (Entropy, (2025), 27, 3, (225), 10.3390/e27030225)

In Proposition 1 of [1], the sufficient condition for stochastic degradedness was stated incorrectly. The correct condition corresponding to (Formula presented.) being stochastically larger than (Formula presented.) is (Formula presented.) for all (Formula presented.). Therefore, Equation (9) should be replaced with (Formula presented.) For the bivariate Rayleigh fading model in Section 3.2, using the complementary cdf (Formula presented.), (Formula presented.), (Formula presented.), the corrected condition yields (Formula presented.). Therefore, Equation (15) should be replaced with (Formula presented.) As a consequence, among the parameter sets originally listed in Table 1, the following parameter sets must be removed: (Formula presented.), (Formula presented.) and (Formula presented.), for all values of (Formula presented.) and (Formula presented.). Accordingly, based on these changes, the following changes have been made to the original publication: In Table 1, only the degraded-case parameter sets should remain, namely, (Table presented.) Figures 2–5 must be updated by removing all subfigures in the top row and, in each remaining bottom-row subfigure, removing the curves corresponding to (Formula presented.). In the legends of Figures 2–5, the entries corresponding to (Formula presented.) must be removed. In Section 5, in the paragraph beginning with “We consider a stochastically degraded secure ISAC channel …, ” the formulation regarding the choice of the considered parameter sets for the degraded-case should be updated and stated more precisely. In Section 5, the paragraph beginning with “We compute the results for (Formula presented.), (Formula presented.), and (Formula presented.) …,” should be updated so that it no longer states that (Formula presented.) is modified from top to bottom and that (Formula presented.) is modified within a subfigure. In Section 5, the discussion should be updated by removing claims that rely on the deleted parameter variations in (Formula presented.) and in the two values of (Formula presented.). In particular, in the paragraph beginning with “We next list our conclusions for a degraded secure ISAC channel …,” the following sentence should be removed: “The numerical results also indicate that (8b) as a summand of (Formula presented.) does not depend on (Formula presented.) and (Formula presented.).”. In the paragraph beginning with “Furthermore, we observe the following monotonicities …,” the sentence “Furthermore, we observe the following monotonicities: (Formula presented.) increases for increasing parameters (Formula presented.) or (Formula presented.) and for decreasing parameters (Formula presented.) or (Formula presented.).” should be replaced with the sentence “Furthermore, we observe the following monotonicities: (Formula presented.) increases for increasing parameter (Formula presented.) and for decreasing parameter (Formula presented.).”. Moreover, in the last paragraph beginning with “The interesting regime where the channel capacity is approached …,” the sentences “The range for the power P where (Formula presented.) determines (8) increases with increasing (Formula presented.) or (Formula presented.) and decreasing (Formula presented.) or (Formula presented.). For low correlation (Formula presented.), this range stretches over all considered power values for almost all parameter constellations, whereas for highly correlated fading coefficients it shrinks to low power values. Thus, in the low power regime, channel capacity is approached irrespective of the values of the remaining parameters.” should be replaced with the sentences “Figures 2–5 show that the range of power P for which the channel capacity is approached stretches over all considered power values except when the power correlation coefficient (Formula presented.) is high combined with a low fading parameter (Formula presented.), as can be observed in the leftmost diagrams of Figures 4 and 5. Thus, we observe that in the low power regime, channel capacity is always approached irrespective of the values of the remaining parameters.”. In Table 1, only the degraded-case parameter sets should remain, namely, (Table presented.) Parameter sets for numerical calculations. Figures 2–5 must be updated by removing all subfigures in the top row and, in each remaining bottom-row subfigure, removing the curves corresponding to (Formula presented.). In the legends of Figures 2–5, the entries corresponding to (Formula presented.) must be removed. In Section 5, in the paragraph beginning with “We consider a stochastically degraded secure ISAC channel …, ” the formulation regarding the choice of the considered parameter sets for the degraded-case should be updated and stated more precisely. In Section 5, the paragraph beginning with “We compute the results for (Formula presented.), (Formula presented.), and (Formula presented.) …,” should be updated so that it no longer states that (Formula presented.) is modified from top to bottom and that (Formula presented.) is modified within a subfigure. In Section 5, the discussion should be updated by removing claims that rely on the deleted parameter variations in (Formula presented.) and in the two values of (Formula presented.). In particular, in the paragraph beginning with “We next list our conclusions for a degraded secure ISAC channel …,” the following sentence should be removed: “The numerical results also indicate that (8b) as a summand of (Formula presented.) does not depend on (Formula presented.) and (Formula presented.).”. In the paragraph beginning with “Furthermore, we observe the following monotonicities …,” the sentence: “Furthermore, we observe the following monotonicities: (Formula presented.) increases for increasing parameters (Formula presented.) or (Formula presented.) and for decreasing parameters (Formula presented.) or (Formula presented.).” should be replaced with the sentence: “Furthermore, we observe the following monotonicities: (Formula presented.) increases for increasing parameter (Formula presented.) and for decreasing parameter (Formula presented.).”. Moreover, in the last paragraph beginning with “The interesting regime where the channel capacity is approached …,” the sentences: “The range for the power P where (Formula presented.) determines (8) increases with increasing (Formula presented.) or (Formula presented.) and decreasing (Formula presented.) or (Formula presented.). For low correlation (Formula presented.), this range stretches over all considered power values for almost all parameter constellations, whereas for highly correlated fading coefficients it shrinks to low power values. Thus, in the low power regime, channel capacity is approached irrespective of the values of the remaining parameters.” should be replaced with the sentences: “Figures 2–5 show that the range of power P for which the channel capacity is approached stretches over all considered power values except when the power correlation coefficient (Formula presented.) is high combined with a low fading parameter (Formula presented.), as can be observed in the leftmost diagrams of Figures 4 and 5. Thus, we observe that in the low power regime, channel capacity is always approached irrespective of the values of the remaining parameters.”. “The numerical results also indicate that (8b) as a summand of (Formula presented.) does not depend on (Formula presented.) and (Formula presented.).”. “Furthermore, we observe the following monotonicities: (Formula presented.) increases for increasing parameters (Formula presented.) or (Formula presented.) and for decreasing parameters (Formula presented.) or (Formula presented.).” “Furthermore, we observe the following monotonicities: (Formula presented.) increases for increasing parameter (Formula presented.) and for decreasing parameter (Formula presented.).”. “The range for the power P where (Formula presented.) determines (8) increases with increasing (Formula presented.) or (Formula presented.) and decreasing (Formula presented.) or (Formula presented.). For low correlation (Formula presented.), this range stretches over all considered power values for almost all parameter constellations, whereas for highly correlated fading coefficients it shrinks to low power values. Thus, in the low power regime, channel capacity is approached irrespective of the values of the remaining parameters.” “Figures 2–5 show that the range of power P for which the channel capacity is approached stretches over all considered power values except when the power correlation coefficient (Formula presented.) is high combined with a low fading parameter (Formula presented.), as can be observed in the leftmost diagrams of Figures 4 and 5. Thus, we observe that in the low power regime, channel capacity is always approached irrespective of the values of the remaining parameters.”. The authors state that the scientific conclusions are unaffected. This correction was approved by the Academic Editor. The original publication has also been updated.