Analysis of Mismatched Estimation Errors Using Gradients of Partition Functions

DOI10.1109/TIT.2014.2301436zbMATH Open1360.94075arXiv1306.0094OpenAlexW2002870244MaRDI QIDQ2986441

Publication date: 16 May 2017

Published in: IEEE Transactions on Information Theory (Search for Journal in Brave)

Abstract: 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. The paper consists of essentially two parts. In the first part, using the aforementioned relationship, we derive single-letter expressions of the 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.

Full work available at URL: https://arxiv.org/abs/1306.0094

Mathematics Subject Classification ID

Signal theory (characterization, reconstruction, filtering, etc.) (94A12)