The rate-distortion infimum is attained for lower semi-continuous distortions on locally compact Polish alphabets via one-point compactification for bounded distortions and concentration-compactness for unbounded coercive distortions.
ThenZ BR0 (xm) dµm + Z BR(ym) dµm ≥Q m(R0) +Q m(R)− 2 m →Q(R 0) +Q(R) > 1 2 + 1 2 = 1 = Z X dµm,(15) for all sufficiently largem
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Rate-distortion Theory with Lower Semi-continuous Distortion on Noncompact Alphabets
The rate-distortion infimum is attained for lower semi-continuous distortions on locally compact Polish alphabets via one-point compactification for bounded distortions and concentration-compactness for unbounded coercive distortions.