On Detection With Partial Information In The Gaussian Setup

TL;DR

This paper investigates detection in Gaussian noise with partial, dimension-reduced information at the receiver, deriving optimal detection rules and quantifying the best linear transforms to minimize error probabilities.

Contribution

It introduces a new detection framework with partial information, deriving MAP detection rules and identifying optimal linear transforms to improve detection performance.

Findings

Derived MAP detection rule for partial information setup.

Quantified optimal linear transforms minimizing Chernoff bound.

Provided analytical expressions for conditional error probabilities.

Abstract

We introduce the problem of communication with partial information, where there is an asymmetry between the transmitter and the receiver codebooks. Practical applications of the proposed setup include the robust signal hashing problem within the context of multimedia security and asymmetric communications with resource-lacking receivers. We study this setup in a binary detection theoretic context for the additive colored Gaussian noise channel. In our proposed setup, the partial information available at the detector consists of dimensionality-reduced versions of the transmitter codewords, where the dimensionality reduction is achieved via a linear transform. We first derive the corresponding MAP-optimal detection rule and the corresponding conditional probability of error (conditioned on the partial information the detector possesses). Then, we constructively quantify an optimal class of linear transforms, where the cost function is the expected Chernoff bound on the conditional probability of error of the MAP-optimal detector.