We study the information bottleneck (IB) source coding problem, also known as remote lossy source coding under logarithmic loss. Based on a rate-limited description of noisy observations, the receiver produces a soft estimate for the remote source, i.e., a probability distribution, evaluated under the logarithmic loss. We focus on the excess distortion probability of IB source coding and investigate how fast it converges to 0 or 1, depending on whether the rate is above or below the rate-distortion function. The latter case is also known as the exponential strong converse. We establish both the exact error exponent and the exact strong converse exponent for IB source coding by deriving matching upper and lower exponential bounds. The obtained exponents involve optimizations over auxiliary random variables. The matching converse bounds are derived through non-trivial extensions of existing sphere packing and single-letterization techniques, which we adapt to incorporate auxiliary random variables. In the second part of this paper, we establish a code-level connection between IB source coding and source coding with a helper, also known as the Wyner-Ahlswede-K\"orner (WAK) problem. We show that every code for the WAK problem is a code for IB source coding. This requires noticing that IB source coding, under the excess distortion criterion, is equivalent to source coding with a helper available at both the transmitter and the receiver; the latter in turn relates to the WAK problem. Through this connection, we re-derive the best known sphere packing exponent of the WAK problem, and provide it with an operational interpretation.

翻译：本文研究了信息瓶颈（IB）信源编码问题，该问题也被称为对数损失下的远程有损信源编码。基于对噪声观测的速率受限描述，接收端为远程信源生成一个软估计，即一个概率分布，该估计在对数损失下进行评估。我们重点关注IB信源编码的超额失真概率，并研究其收敛到0或1的速度，这取决于速率是高于还是低于率失真函数。后一种情况也被称为指数强逆定理。通过推导匹配的上、下指数界，我们为IB信源编码建立了精确的误差指数和精确的强逆指数。所获得的指数涉及对辅助随机变量的优化。匹配的逆界是通过对现有球堆积和单字母化技术的非平凡扩展推导得出的，我们对其进行了调整以纳入辅助随机变量。在本文的第二部分，我们建立了IB信源编码与辅助信源编码（也称为Wyner-Ahlswede-Körner（WAK）问题）之间的编码级联系。我们证明了WAK问题的每一个编码都是IB信源编码的一个编码。这需要注意到，在超额失真准则下，IB信源编码等价于在发送端和接收端均存在辅助信息的信源编码；而后者又与WAK问题相关。通过这一联系，我们重新推导了WAK问题中已知的最佳球堆积指数，并为其提供了操作解释。