Involved in the degradation of terephthalate (TPA) via the protocatechuate (PCA) 4,5-cleavage pathway. Catalyzes the dehydrogenation of 1,2-dihydroxy-3,5-cyclohexadiene-1,4-dicarboxylate (DCD) to yield protocatechuate (PCA). (3S,4R)-3,4-dihydroxycyclohexa-1,5-diene-1,4-dicarboxylate + NAD(+) = 3,4-dihydroxybenzoate + CO2 + NADH Belongs to the PdxA family.