基于信息保真度的通信系统信息恢复性能界限

Information Fidelity-Based Performance Bounds for Information Recovery in Communication Systems

摘要

针对通信系统信号传输过程中先验信息损失导致性能评估失真的问题, 提出一种基于信息保真度的信息恢复性能界限评估方法。 在实际通信环境中, 由于信道噪声和系统非理想性, 接收端通常无法获取完整的发送端先验信息, 其使传统基于 Fisher 信息的 Cramér-Rao 界限适用性受到限制。 通过引入信息保真度及其矩母函数, 建立了噪声-信号比(NSR: Noise-to-Signal Ratio)与 Fisher 信息、 保真度信息间的下界不等式关系, 并构造了新的噪信比下界估计模型, 为通信系统的信息恢复性能提供了更为稳健的理论界限。 理论分析和两个数值算例(包括二进制通信系统与多模信号传输信道)表明, 相比经典的 Fisher 信息界限, 基于信息保真度的界限虽然更为宽松, 但在先验信息不完整、 小样本等实际通信场景中具有更强的稳健性和实用性, 并为通信系统性能评估提供了新的理论工具。

Abstract

To address the performance distortion caused by a priori information loss in signal transmission processes of communication systems, an information fidelity-based performance bounds evaluation method is proposed for information recovery. In practical communication environments, due to channel noise and system non-ideality, the receiver often can not obtain a complete priori information from the transmitter, which limits the applicability of traditional Fisher-information-based Cramér-Rao bounds under such conditions. By introducing the concept of information fidelity and its moment generating function, an inequality relating the noise-to-signal ratio, the Fisher information, and the fidelity information is established, and a new lower-bound estimation model for NSR(Noise-to-Signal Ratio) is derived, providing more robust theoretical bounds for information recovery performance in communication systems. Theoretical analysis and two numerical examples (including a binary communication system and a multimode signal transmission channel) demonstrate that, compared with classical Fisher-information-based bounds, the information-fidelity-based bounds, while more relaxed, exhibit stronger robustness and practicality in realistic scenarios with incomplete a priori information, and small sample sizes, offering a new theoretical tool for communication system performance evaluation.

关键词

通信系统 / 信息保真度 / 信息恢复 / 性能界限 / Fisher 信息 / Cramér-Rao 不等式

Key words

communication systems / information fidelity / information recovery / performance bounds / Fisher information / Cramér-Rao inequality

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