We study task-oriented lossy compression through the lens of rate-distortion-classification (RDC) representations. The source is Bernoulli, the distortion measure is Hamming, and the binary classification variable is coupled to the source via a binary symmetric model. Building on the one-shot common-randomness formulation, we first derive closed-form characterizations of the one-shot RDC and the dual distortion-rate-classification (DRC) tradeoffs. We then use a representation-based viewpoint and characterize the achievable distortion-classification (DC) region induced by a fixed representation by deriving its lower boundary via a linear program. Finally, we study universal encoders that must support a family of DC operating points and derive computable lower and upper bounds on the minimum asymptotic rate required for universality, thereby yielding bounds on the corresponding rate penalty. Numerical examples are provided to illustrate the achievable regions and the resulting universal RDC/DRC curves.

翻译：本研究通过率失真分类（RDC）表示的视角探讨面向任务的失真压缩问题。信源为伯努利分布，失真度量采用汉明距离，二元分类变量通过二元对称模型与信源耦合。基于单次共同随机性框架，我们首先推导了单次RDC及其对偶问题——失真率分类（DRC）权衡的闭式表征。随后采用基于表示的观点，通过线性规划推导固定表示所诱导的失真分类（DC）可达区域下边界，从而完整刻画该区域。最后，我们研究了需支持一族DC工作点的通用编码器，推导了实现通用性所需最小渐近速率的可计算上下界，进而得到相应速率惩罚的界。数值算例展示了可达区域及由此生成的通用RDC/DRC曲线。