Information-Theoretic Bounds in Source Coding and Guessing
Summary
Information‐theoretic bounds in source coding and guessing lie at the heart of quantifying uncertainty, compression efficiency and search complexity. In source coding, Shannon’s entropy and its generalisations measure the minimal average description length of a random source, while Rényi entropy parameters govern non‐asymptotic and exponential‐moment criteria. In parallel, guessing problems characterise the effort required to identify an unknown outcome by sequential queries, with performance assessed via moments of the number of guesses. Fundamental results establish that optimal coding and guessing strategies minimise suitable entropy measures, leading to tight asymptotic and non‐asymptotic bounds. These theoretical limits underpin practical applications in data compression, cryptography and networked inference, where resource constraints and side information influence both code design and search protocols. Recent work has extended classical inequalities—such as Fano’s and Pinsker’s—to Rényi and guessing‐entropy settings, unified disparate tasks under a common moment‐minimisation framework and characterised finite‐blocklength trade‐offs via cumulant generating functions. Together, these advances enhance our understanding of how randomness, error tolerance and computational effort interact across diverse information‐processing scenarios.
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Information-Theoretic Bounds in Source Coding and Guessing publication trend
The graph below shows the total number of articles in information-theoretic bounds in source coding and guessing across all publications each year (not limited to Nature Index journals).
Technical terms
Shannon entropy: A measure of the average unpredictability or information content of a discrete random source.
Rényi entropy: A one‐parameter family of entropy measures generalising Shannon entropy, emphasising different tail behaviours of the probability distribution.
Cumulant generating function: A transform that summarises all moments of a random variable, used to derive non‐asymptotic bounds on codeword lengths.
Guessing entropy: The expected logarithm of the number of sequential queries required to identify a random outcome under an optimal strategy.
Error exponent: The rate at which the probability of decoding or guessing error decays exponentially with blocklength.
Total‐variation distance: A metric quantifying the maximum difference between two probability distributions over all events.
References
- Are Guessing, Source Coding and Tasks Partitioning Birds of A Feather? †. Entropy (2022).
- Non-Asymptotic Bounds of Cumulant Generating Function of Codeword Lengths in Variable-Length Lossy Compression. IEEE Transactions on Information Theory (2022).
- The Interplay between Error, Total Variation, Alpha-Entropy and Guessing: Fano and Pinsker Direct and Reverse Inequalities §. Entropy (2023).
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