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Updated: Jun 27, 2026
13:04
Experimental and Data Analysis Workflow for Soft Matter Nanoindentation
Published on: January 18, 2022
A Statistical-Physics Refinement of Soft Covering
1The Viterbi Faculty of Electrical and Computer Engineering, Technion-Israel Institute of Technology, Technion City, Haifa 3200003, Israel.
Entropy (Basel, Switzerland)
|June 26, 2026
Summary
We analyze random codes using statistical physics, revealing two distinct codeword behaviors: typical (bulk) and atypical (sparse). Their competition defines a phase diagram with implications for information theory applications.
Area of Science:
- Information Theory
- Statistical Physics
- Coding Theory
Background:
- Studying channel output distributions is crucial for understanding information transmission.
- Random codes are fundamental in coding theory, but their output distributions are complex.
- Statistical physics offers powerful tools for analyzing complex systems, including random codes.
Purpose of the Study:
- To analyze the channel output distribution induced by random codes using statistical physics.
- To investigate the annealed free energy and its connection to the Rényi spectrum.
- To characterize the competition between typical (bulk) and atypical (sparse) codewords.
Main Methods:
- Utilized statistical physics concepts, including partition functions and annealed free energy.
- Derived a single-letter formula for the annealed free energy, decomposing it into bulk and sparse branches.
- Analyzed the phase structure of each branch and their competition, defining transition boundaries.
Main Results:
- The annealed free energy encodes the full Rényi spectrum of the output distribution.
- A phase diagram is established with four regions defined by bulk and sparse branch transitions.
- The competition boundary R*(β) between bulk and sparse branches has a closed-form expression for β≥1.
Conclusions:
- The study provides a novel statistical physics framework for analyzing random codes.
- The identified bulk and sparse branches offer insights into codeword behavior and competition.
- Results have potential applications in guesswork, channel resolvability, and hypothesis testing.
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