A comment on “A rate of convergence result for a universal D-semifaithful code”

In the above paper (see ibid., vol.39, no.3, p.813-20, 1993) Yu and Speed propose a universal pointwise D-semifaithful code whose expected compression ratio, for discrete memoryless sources, approaches the rate-distortion function at a rate O(n^-1 log n). They also conjecture that this is the fastest achievable convergence rate for pointwise D-semifaithful codes. In this correspondence, we use a simple extension of Kraft´s inequality and prove that this conjecture is true, at least for the Ramming distortion measure