Semantic communication is a novel communication paradigm that focuses on conveying the user's intended meaning rather than the bit-wise transmission of source signals. One of the key challenges is to effectively represent and extract the semantic meaning of any given source signals. While deep learning (DL)-based solutions have shown promising results in extracting implicit semantic information from a wide range of sources, existing work often overlooks the high computational complexity inherent in both model training and inference for the DL-based encoder and decoder. To bridge this gap, this paper proposes a rate-distortion-complexity (RDC) framework which extends the classical rate-distortion theory by incorporating the constraints on semantic distance, including both the traditional bit-wise distortion metric and statistical difference-based divergence metric, and complexity measure, adopted from the theory of minimum description length and information bottleneck. We derive the closed-form theoretical results of the minimum achievable rate under given constraints on semantic distance and complexity for both Gaussian and binary semantic sources. Our theoretical results show a fundamental three-way tradeoff among achievable rate, semantic distance, and model complexity. Extensive experiments on real-world image and video datasets validate this tradeoff and further demonstrate that our information-theoretic complexity measure effectively correlates with practical computational costs, guiding efficient system design in resource-constrained scenarios.

翻译：语义通信是一种新型通信范式，其核心在于传递用户意图的含义，而非源信号的比特级传输。关键挑战之一在于如何有效表征和提取任意给定源信号的语义信息。尽管基于深度学习的方法在从广泛信源中提取隐式语义信息方面展现出良好前景，现有研究往往忽视深度学习编码器与解码器在模型训练和推理过程中固有的高计算复杂度。为弥补这一空白，本文提出速率-失真-复杂度理论框架，该框架通过引入语义距离约束（包含传统比特级失真度量与基于统计差异的散度度量）以及源自最小描述长度理论与信息瓶颈理论的复杂度度量，对经典率失真理论进行了拓展。我们推导出高斯与二进制语义信源在给定语义距离与复杂度约束下可实现最小速率的闭式理论解。理论结果表明，在可达速率、语义距离与模型复杂度之间存在根本性的三维权衡关系。在真实图像与视频数据集上的大量实验验证了该权衡关系，并进一步证明我们提出的信息论复杂度度量与实际计算成本有效关联，可为资源受限场景下的高效系统设计提供指导。