2011/09/01 by Tsachy Weissman, Weissman, Tsachy, Young-Han Kim +3 · 2 citations
Computer Science · Engineering · Physics and Astronomy · #Distributed Sensor Networks and Detection Algorithms #FOS: Computer and information sciences #Information Theory (cs.IT) #Molecular Communication and Nanonetworks #Quantum Mechanics and Applications #Wireless Communication Security Techniques
paper · pdf · doi:10.48550/arxiv.1109.0351
openalex publication_date 2011/09/01 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28
A notion of directed information between two continuous-time processes is\nproposed. A key component in the definition is taking an infimum over all\npossible partitions of the time interval, which plays a role no less\nsignificant than the supremum over "space" partitions inherent in the\ndefinition of mutual information. Properties and operational interpretations in\nestimation and communication are then established for the proposed notion of\ndirected information. For the continuous-time additive white Gaussian noise\nchannel, it is shown that Duncan's classical relationship between causal\nestimation and information continues to hold in the presence of feedback upon\nreplacing mutual information by directed information. A parallel result is\nestablished for the Poisson channel. The utility of this relationship is then\ndemonstrated in computing the directed information rate between the input and\noutput processes of a continuous-time Poisson channel with feedback, where the\nchannel input process is constrained to be constant between events at the\nchannel output. Finally, the capacity of a wide class of continuous-time\nchannels with feedback is established via directed information, characterizing\nthe fundamental limit on reliable communication.\n