Two strong converses are obtained for an abstract alphabet stationary ergodic source coded relative to an appropriate fidelity criterion. It is shown that given a distortion rate point (D,R) that lies below the rate distortion curve, (1) block codes that operate at rate level R must encode sample source blocks at a rate exceeding D with probability tending to one as the block length tends to infinity, and (2) variable-rate codes that operate at distortion level D must encode sample source blocks at a rate exceeding R with probability tending to one as the block length tends to infinity. The previously known weak converses guarantee only that the indicated probabilities remain bounded away from zero as block length tends to infinity. The proofs of the strong converses involve sample converses in source coding theory.
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