Abstract
We develop the algebraic theory of timed capacity for channels with binary inputs and outputs in the presence of noise, by obtaining a formula for capacity in terms of the unique solution of a nonlinear algebraic equation. We give provably correct numerical algorithms for solving this equation, specifically tailored toward calculating capacity. We use our results to establish that information theory has an inherent discontinuity in it: the function which assigns the unique capacity achieving distribution to the noise matrix of a binary channel has no continuous extension to the set of all noise matrices. Our results provide new formulae in the case of untimed binary channels as well. Our results are important in the study of real-world systems, such as the NRL Network Pump® system and traffic analysis in anonymity systems.
Research supported by the Naval Research Laboratory.
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Martin, K., Moskowitz, I.S. (2007). Noisy Timing Channels with Binary Inputs and Outputs. In: Camenisch, J.L., Collberg, C.S., Johnson, N.F., Sallee, P. (eds) Information Hiding. IH 2006. Lecture Notes in Computer Science, vol 4437. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74124-4_9
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DOI: https://doi.org/10.1007/978-3-540-74124-4_9
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