Transmission of Information¹

Abstract

Synopsis: A quantitative measure of “information” is developed which is based on physical as contrasted with psychological considerations. How the rate of transmission of this information over a system is limited by the distortion resulting from storage of energy is discussed from the transient viewpoint. The relation between the transient and steady state viewpoints is reviewed. It is shown that when the storage of energy is used to restrict the steady state transmission to a limited range of frequencies the amount of information that can be transmitted is proportional to the product of the width of the frequency‐range by the time it is available. Several illustrations of the application of this principle to practical systems are included. In the case of picture transmission and television the spacial variation of intensity is analyzed by a steady state method analogous to that commonly used for variations with time.

Information Theoretic Security for Encryption Based on Conditional Rényi Entropies

“…Historically, Shannon entropy [2] is the measure of information theoretic cryptography. On the other hand, it is also important to evaluate the cardinality of a set in which a random variable takes values, i.e., Hartley entropy [3]. Furthermore, minentropy [4] is also considered to be an important quantity in guessing the secret in the context of cryptography.…”

“…Furthermore, Dodis [6] recently showed that the similar property also holds with respect to min-entropy. Namely, he showed the bound on secret-keys, R ∞ (K) ≥ R ∞ (M ), for symmetric-key encryption with perfect secrecy 3 . Also, Alimomeni and Safavi-Naini [8] introduced the guessing secrecy, formalized by R ∞ (M ) = R ∞ (M |C), and under which they derived the bound R ∞ (K) ≥ R ∞ (M ), where R ∞ (·) and R ∞ (·|·) are the min-entropy and the conditional min-entropy, respectively.…”

Possibilistic Graphical Models

“…The measure of nonspecificity can be derived from Hartley information [25], in contrast to some evaluation measures for learning probabilistic networks, which are based on Shannon information [45]. In order to arrive at an efficient algorithm, an approximation for this loss of specificity is derived, which can be computed locally on the maximal cliques of the network.…”

Some experimental results on learning probabilistic and possibilistic networks with different evaluation measures

“…and can be justified as a generalization of Hartley information [10] to the possibilistic setting [13]. nsp(π) reflects the expected amount of information (measured in bits) that has to be added in order to identify the actual value within the set [π] α of alternatives, assuming a uniform distribution on the set [0, sup(π)] of possibilistic confidence levels α [9].…”