2022/02/20 by Mohsen Heidari, Heidari, Mohsen, Achilleas Anastasopoulos +3
Biochemistry, Genetics and Molecular Biology · Computer Science · Engineering · #Computability, Logic, AI Algorithms #DNA and Biological Computing #FOS: Computer and information sciences #Information Theory (cs.IT) #Wireless Communication Security Techniques
paper · pdf · doi:10.48550/arxiv.2202.09933
openalex publication_date 2022/02/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
As a class of state-dependent channels, Markov channels have been long studied in information theory for characterizing the feedback capacity and error exponent. This paper studies a more general variant of such channels where the state evolves via a general stochastic process, not necessarily Markov or ergodic. The states are assumed to be unknown to the transmitter and the receiver, but the underlying probability distributions are known. For this setup, we derive an upper bound on the feedback error exponent and the feedback capacity with variable-length codes. The bounds are expressed in terms of the directed mutual information and directed relative entropy. The bounds on the error exponent are simplified to Burnashev's expression for discrete memoryless channels. Our method relies on tools from the theory of martingales to analyze a stochastic process defined based on the entropy of the message given the past channel's outputs.