We propose a mathematical theory of pragmatic information that unifies communication,control,and decision-making within a coherent framework.At its core is the isoteleia mapping,which formalizes equifinality:distinct semantic paths that lead to the same optimal action are regarded as pragmatically equivalent.This mapping induces a three-tier hi-erarchy of syntactic,semantic,and pragmatic information,in which each successive abstraction discards distinctions that are irrelevant to the task.Building on this hierarchy,we develop a set of information-theoretic measures at the pragmatic level,including pragmatic entropy,up/down pragmatic mutual information,channel capacity,and rate-distortion.In ad-dition,we prove three coding theorems—lossless source coding,channel coding,and rate-distortion—which generalize Shannon's classical results.We then introduce pragmatic value of information(VoI)and pragmatic cost of information(CoI)as decision-theoretic duals to rate-distortion and capacity,respectively,and formulate a Lagrangian dual framework for cross-layer optimization.The resulting pragmatic efficiency bound εp(λ)=supR[Φp(R)-λCoIp(R)]characterizes the maximum net utility attainable by a resource-constrained intelligent system under a given resource price,thereby providing a limit on purposeful behavior—abehavioral capacity.This limit can be viewed as a goal-directed analogue of Shannon's symbol-level capacity under the stated utility and resource assumptions.Extensions to continuous messages yield closed-form expressions for Gaussian channels and sources,while dynamic settings are addressed through a Bellman equation for sequential decision-making.Finally,this framework provides a foundation for task-oriented communication,networked control,autonomous systems,and embodied AI,shifting the focus from symbol fidelity to the effectiveness of information in guiding actions,and offering a mathematical language for the design of next-generation intelligent systems.
To address the high PAPR and RSSL caused by random modulation in integrated sensing and communication, this paper proposes a PRS-IM-based low-PAPR waveform design method. Integrating PRS, IM, and QAM, a PRS-IM-QAM waveform structure is constructed. Under reliable communication power constraints, a joint PSLR and PAPR optimization model is established. For the nonconvex minimax fractional PSLR optimization problem, the Charnes-Cooper transform converts it into a second-order cone programming convex problem. For PAPR optimization, a TLADMM algorithm with inner-loop iterations reduces computational cost. Results show that PRS-IM-QAM reduces RSSL from about -35 dB to -45 dB and PAPR to about 4.5 dB. Its communication performance is slightly worse than 16QAM. Compared with the PRS benchmark, it sacrifices only about 0.75 m range resolution while significantly improving weak-target detection by approximately 20 dB.
To solve the challenge that blockchain network anomaly detection struggles to cope with the dynamic evolution of attacks and normal behaviors, this paper proposes a blockchain anomaly detection technology based on sample space reconstruction. The method can identify the statistical distribution shift in the sample space and avoid catastrophic forgetting during model updates. The core idea of the technique is as follows. First, a temporal autoencoder is used to unsupervised learn normal traffic and construct the sample space representation of normal behaviors. Second, isotonic regression is introduced to probabilistically calibrate anomaly scores, making detection results from different time windows comparable. KL divergence and permutation tests are adopted to statistically infer traffic distributions, identify sample space shifts caused by normal behaviors, and distinguish normal sample variations from anomalous attacks. Finally, once a shift is detected, the model is updated adaptively. While retaining the memory of normal patterns, new normal samples are incorporated into the sample space. Experimental results show that the proposed blockchain anomaly detection method achieves an average AUC of 0.89. It improves performance by approximately 40% compared with static models, and the false positive rate is reduced by more than 70%.
To reduce uplink packet delay and energy consumption under channel fluctuations and finite-blocklength transmission errors, a stochastic service model incorporating ordered gating and decoding reliability was developed for cell-free massive multiple-input multiple-output systems. A statistical delay bound was derived using stochastic network calculus under sufficient conditions including independence between arrivals and service, and was used as a delay reference threshold under dynamic policies. A network calculus aided proximal policy optimization algorithm was proposed to jointly select user equipment–access point associations, bandwidth, and transmit power by minimizing delay excess and wireless transmission energy consumption. Reductions in delay excess and transmission energy consumption were observed in simulations. The proposed method provides a reference for uplink association and resource optimization subject to statistical delay constraints.
