Elements of information theory
Elements of information theory
An introduction to Kolmogorov complexity and its applications (2nd ed.)
An introduction to Kolmogorov complexity and its applications (2nd ed.)
Information Theory: Coding Theorems for Discrete Memoryless Systems
Information Theory: Coding Theorems for Discrete Memoryless Systems
Concentration Theorems for Entropy and Free Energy
Problems of Information Transmission
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Conditions are presented under which the maximum of the Kolmogorov complexity (algorithmic entropy) K(ω1…ωN) is attained, given the cost \sum_{i=1}^{N} f(ωi) of a message ω1…ωN. Various extremal relations between the message cost and the Kolmogorov complexity are also considered; in particular, the minimization problem for the function \sum_{i=1}^{N} f(ωi) − &thetas;K(ω1…ωN) is studied. Here, &thetas; is a parameter, called the temperature by analogy with thermodynamics. We also study domains of small variation of this function.