A Context-Aware CEO Problem

TL;DR

This paper extends the CEO problem in sensor networks by incorporating context information, characterizing optimal error exponents, and proposing efficient sensor grouping strategies, with numerical validation in Gaussian scenarios.

Contribution

It introduces a generalized CEO problem with context data, deriving asymptotic error exponents and optimal sensor grouping schemes, extending previous models without context.

Findings

Derived the asymptotic error exponent per rate with context information.

Proved optimal sensor grouping into at most rac{|\u00Xx|rac{2}{}}{2} |S| groups.

Numerically demonstrated the impact of context in Gaussian scenarios.

Abstract

In many sensor network applications, a fusion center often has additional valuable information, such as context data, which cannot be obtained directly from the sensors. Motivated by this, we study a generalized CEO problem where a CEO has access to context information. The main contribution of this work is twofold. Firstly, we characterize the asymptotically optimal error exponent per rate as the number of sensors and sum rate grow without bound. The proof extends the Berger-Tung coding scheme and the converse argument by Berger et al. (1996) taking into account context information. The resulting expression includes the minimum Chernoff divergence over context information. Secondly, assuming that the sizes of the source and context alphabets are respectively $|\mathcal{X}|$ and $|\mathcal{S}|$, we prove that it is asymptotically optimal to partition all sensors into at most $\binom{|\mathcal{X}|}{2} |\mathcal{S}|$ groups and have the sensors in each group adopt the same encoding scheme. Our problem subsumes the original CEO problem by Berger et al. (1996) as a special case if there is only one letter for context information; in this case, our result tightens its required number of groups from $\binom{|\mathcal{X}|}{2}+2$ to $\binom{|\mathcal{X}|}{2}$. We also numerically demonstrate the effect of context information for a simple Gaussian scenario.