LZ78 sources are almost stationary ergodic processes satisfying a Shannon-McMillan-Breiman property and local i.i.d. convergence, yet their finite-state compressibility exceeds the entropy rate by a Jensen gap.
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The LZ78 Source
LZ78 sources are almost stationary ergodic processes satisfying a Shannon-McMillan-Breiman property and local i.i.d. convergence, yet their finite-state compressibility exceeds the entropy rate by a Jensen gap.