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.

翻译：在许多传感器网络应用中，融合中心往往拥有额外的宝贵信息（如上下文数据），这些信息无法直接从传感器获取。受此启发，我们研究了一个广义的CEO问题，其中CEO能够获取上下文信息。本文的主要贡献有两方面。首先，我们刻画了当传感器数量和总速率无界增长时，每个速率的渐近最优误差指数。该证明扩展了Berger-Tung编码方案以及Berger等人（1996）的逆向论证，同时考虑了上下文信息。最终表达式包含了上下文信息上的最小Chernoff散度。其次，假设信源和上下文字母表的大小分别为$|\mathcal{X}|$和$|\mathcal{S}|$，我们证明了将所有传感器划分为最多$\binom{|\mathcal{X}|}{2} |\mathcal{S}|$个组，并使每组中的传感器采用相同编码方案是渐近最优的。若上下文信息仅包含单个字母，我们的问题退化为Berger等人（1996）的原始CEO问题；在此情况下，我们将所需组数从$\binom{|\mathcal{X}|}{2}+2$缩减至$\binom{|\mathcal{X}|}{2}$。最后，我们通过简单高斯场景数值展示了上下文信息的影响。