ERC Advanced Grant · 2023
Scaling and Concentration Laws in Information Theory
Shannon’s 1948 paper established the mathematical foundations of digital compression and transmission and paved the way for the information age. A notion embedded in Shannon’s and most work in Information Theory is the concept of rate, defined as the exponential growth rate of the number of messages. The probabilistic law governing general information processing systems may be such that the optimal number of messages does not scale exponentially with the length of the sequences. The vast majority of the Information Theory literature assumes an exponential number of messages and thus, ignores the rich amount of possible scaling functions in important settings. When the system probability law…
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