Successful communication in daily life depends on accurate decoding of speech signals that are acoustically degraded by challenging listening conditions. This process presents the brain with a demanding computational task that is vulnerable to neurodegenerative pathologies. However, despite recent intense interest in the link between hearing impairment and dementia, comprehension of acoustically degraded speech in these diseases has been little studied. Here we addressed this issue in a cohort of 19 patients with typical Alzheimer's disease and 30 patients representing the three canonical syndromes of primary progressive aphasia (non-fluent/agrammatic variant primary progressive aphasia; semantic variant primary progressive aphasia; logopenic variant primary progressive aphasia), compared to 25 healthy age-matched controls. As a paradigm for the acoustically degraded speech signals of daily life, we used noise-vocoding: synthetic division of the speech signal into frequency channels constituted from amplitude-modulated white noise, such that fewer channels convey less spectrotemporal detail thereby reducing intelligibility. We investigated the impact of noise-vocoding on recognition of spoken three-digit numbers and used psychometric modelling to ascertain the threshold number of noise-vocoding channels required for 50% intelligibility by each participant. Associations of noise-vocoded speech intelligibility threshold with general demographic, clinical and neuropsychological characteristics and regional grey matter volume (defined by voxel-based morphometry of patients' brain images) were also assessed. Mean noise-vocoded speech intelligibility threshold was significantly higher in all patient groups than healthy controls, and significantly higher in Alzheimer's disease and logopenic variant primary progressive aphasia than semantic variant primary progressive aphasia (all P < 0.05). In a receiver operating characteristic analysis, vocoded intelligibility threshold discriminated Alzheimer's disease, non-fluent variant and logopenic variant primary progressive aphasia patients very well from healthy controls. Further, this central hearing measure correlated with overall disease severity but not with peripheral hearing or clear speech perception. Neuroanatomically, after correcting for multiple voxel-wise comparisons in predefined regions of interest, impaired noise-vocoded speech comprehension across syndromes was significantly associated (P < 0.05) with atrophy of left planum temporale, angular gyrus and anterior cingulate gyrus: a cortical network that has previously been widely implicated in processing degraded speech signals. Our findings suggest that the comprehension of acoustically altered speech captures an auditory brain process relevant to daily hearing and communication in major dementia syndromes, with novel diagnostic and therapeutic implications.