For memoryless and Markov sources, the block length needed for lossless compression with bounded rate and excess-rate probability is characterized, up to constants, by the Rényi divergence of order 1/2 from the uniform distribution.
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The Sample Complexity of Lossless Data Compression
For memoryless and Markov sources, the block length needed for lossless compression with bounded rate and excess-rate probability is characterized, up to constants, by the Rényi divergence of order 1/2 from the uniform distribution.