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In this paper, we describe the expected performance of ALADDIN, a nulling interferometer project optimised for operation at Dome C. After reviewing the main atmospheric parameters pertaining to infrared interferometry on the high Antarctic plateau, we shortly describe the ALADDIN instrument and compute its estimated performance in terms of the smallest exozodiacal dust disc density that can be detected. Our estimations are based on a thorough end-to-end software simulator previously developed for the GENIE nulling interferometer project at VLTI. We then propose a possible mission scenario, where the southern target stars of future exo-Earth characterisation missions can be surveyed for the presence of bright exozodiacal discs (>50 zodi) within one winter-over at Concordia. [ABSTRACT FROM AUTHOR]