Comments on "Maximum diversity in single-carrier frequency-domain Equalization"

It was claimed in the above correspondence that "single-carrier frequency-domain equalization (SC-FDE) is capable of collecting full multipath diversity even without channel coding." However, this is not correct because Proposition 2 and Theorem 1 of the above correspondence, which lead to the claim, are both incorrect. In this correspondence, Proposition 2 and Theorem 1 are disproved. As a consequence, the main claim of the above correspondence is denied. Furthermore, a new theorem is given to show that the multipath diversity cannot be achieved by SC-FDE without channel coding. An example is also presented to disprove the main claim of of the above correspondence meanwhile supporting the new theorem proposed in this correspondence