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Relations Between Random Coding Exponents and the Statistical Physics of Random Codes

Overview The partition function pertaining to finite - temperature decoding of a (typical) randomly chosen code is known to have three types of behavior, corresponding to three phases in the plane of rate vs. temperature: the ferromagnetic phase, corresponding to correct decoding, the paramagnetic phase, of complete disorder, which is dominated by exponentially many incorrect codewords, and the glassy phase (or the condensed phase), where the system is frozen at minimum energy and dominated by subexponentially many incorrect codewords. The paper shows that the statistical physics associated with the two latter phases are intimately related to random coding exponents.

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Publisher: Hewlett-Packard (HP)
File Format: PDF
Date Published: Feb 15, 2008
Format: White Papers
Topics: Programming Languages

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