In this paper, we study rate-distortion theory for general sources with an emphasis on the existence of optimal reconstruction distributions. Classical existence results rely on compactness assumptions that are often violated in non-compact settings. By introducing the concentration-compactness principle into the analysis of the rate-distortion functional, we establish the existence of optimal reconstructions under mild coercivity conditions on the distortion function. Our results provide a unified and transparent existence theorem for rate-distortion problems on general non-compact spaces.

翻译：本文研究一般信源的率失真理论，重点探讨最优重建分布的存在性问题。经典的存在性结果依赖于紧性假设，这在非紧空间中往往无法满足。通过将集中紧性原理引入率失真泛函的分析，我们在失真函数满足温和强制性条件下，建立了最优重建分布的存在性。我们的结果为一般非紧空间上的率失真问题提供了一个统一且清晰的存在性定理。