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An achievable bound for optimal noiseless coding of a random variable (Corresp.)

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For a discrete N -valued random variable ( N possibly denumerably infinite) Leung-Yan-Cheong and Cover have given bounds for the minimal expected length of a one-to-one (not necessarily uniquely decodable) code L_{1:1}=\sum _{i=1}^{N} p_{i} \log \left( frac{1}{2} + 1 \right). It is shown that the best possible case occurs for certain denumerably infinite sets of nonzero probabilities. This absolute bound is related to the Shannon entropy H of the distribution by (h (\cdot) is the binary entropy function).

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Information Theory, IEEE Transactions on  (Volume:32 ,  Issue: 4 )