Universal capacity of channels with given rate-distortion in absence of common randomness, and failure of universal source-channel separation

Recently studied the universal capacity of a set of channels where each channel in the set communicates a random source to within a distortion level D, when the transmitter and receiver have access to common randomness. In this paper, we study the universal capacity for this channel set in the case when there is no access to common randomness. We show that when the distortion level D is positive, the universal capacity is 0. This also leads to the conclusion that universal source-channel separation for rate-distortion as stated in, is false.