# An Explainable Deep Semantic Coding for Binary-Classification-Oriented Communication
## 1 Introduction
A federated semantic learning (FedSem) framework is introduced in [21], which collaboratively trains semantic-channel encoders of multiple devices to enable semantic knowledge graph construction with privacy preservation. These studies on semantic coding leverage deep learning methods to extract task-critical features. However, most approaches operate as black-boxes, lacking explainability of the coding scheme [22; 23]. To address this limitation, recent research has explored explainable semantic communication. For example, [24] models control signals as semantic information and proposes a real-time control-oriented semantic communication framework that enables interpretable data transmission. However, this approach is not well-suited for transmitting image data. In [25], a triplet-based representation for text semantics is introduced, incorporating syntactic dependency analysis to enhance interpretability in semantic extraction. However, this method is specifically tailored for text semantics and is not applicable to image-related tasks. The authors in [26] present two information-theoretic metrics to characterize semantic information compression and select only task-critical features. However, these explainable semantic coding methods primarily focus on semantic extraction while overlooking effective data compression, which is crucial for ensuring reliable information transmission in communication systems. In this paper, we propose a theoretically grounded and explainable deep semantic coding framework in a binary-classification-oriented communication (BCOC) scenario. Based on two fundamental information theoretic principles, rate-distortion theory and large-deviation theory, we formulate an optimization problem to effectively balance data compression efficiency and classification accuracy. Furthermore, we leverage deep learning techniques and variational methods to transform the theoretical optimization problem into a deep variational semantic coding (DVSC) model and develop a novel DVSC-Opt algorithm to efficiently obtain the deep semantic coding design. The contributions of this work are summarized as follows. * We formulate an optimization problem in the BCOC scenario from an information-theoretic perspective, addressing both source compression and task-critical information preservation under predefined distortion constraints. By explicitly optimizing a task-discriminative information measure, our framework effectively preserves the information that is critical to the binary classification task in an explainable manner. * We develop the DVSC model with respect to the formulated theoretical optimization problem. Without knowledge of probability distributions, we introduce discriminator networks to facilitate the estimation of information-theoretic terms. Additionally, we propose an efficient training algorithm for deep semantic coding design. * We conduct experimental validation on the CelebA dataset and the CIFAR-10 dataset, demonstrating that the proposed coding scheme effectively balances compression rate and classification accuracy while ensuring acceptable distortions. Notably, the DVSC model is a combination of information-theoretic principles and deep learning techniques. Although hybrid frameworks such as InfoGAN [27] and deep information bottleneck (Deep IB) [28] have been widely adopted in representation learning and generative modeling, their problem formulations differ fundamentally from ours. InfoGAN is designed to learn disentangled representations by maximizing the mutual information between latent codes and generated samples in a generative adversarial framework, without explicitly addressing compression efficiency or task relevance. Deep IB, on the other hand, seeks to extract task-relevant features by optimizing an information bottleneck objective, but it is primarily used in supervised learning contexts and does not consider distortion constraints.