Analysis of mismatched estimation errors using gradients of partition functions

Wasim Huleihel, Neri Merhav

Research output: Contribution to journalArticlepeer-review


We consider the problem of signal estimation (denoising) from a statistical-mechanical perspective, in continuation to a recent work on the analysis of mean-square error (MSE) estimation using a direct relationship between optimum estimation and certain partition functions. This paper consists of essentially two parts. In the first part, using the aforementioned relationship, we derive single-letter expressions of the asymptotic mismatched MSE of a codeword (from a randomly selected code), corrupted by a Gaussian vector channel. In the second part, we provide several examples to demonstrate phase transitions in the behavior of the MSE. These examples enable us to understand more deeply and to gather intuition regarding the roles of the real and the mismatched probability measures in creating these phase transitions.

Original languageEnglish
Article number6717013
Pages (from-to)2190-2216
Number of pages27
JournalIEEE Transactions on Information Theory
Issue number4
StatePublished - Apr 2014
Externally publishedYes


  • Minimum mean-square error (MMSE)
  • conditional mean estimation
  • mismatched MSE
  • partition function
  • phase transitions
  • statistical mechanics
  • threshold effect


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