On dispersion of compound DMCs
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Polyanskiy_On dispersion.pdf
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Author(s)
Polyanskiy, Yury
Date Issued
October 2013
Journal
Proceedings of the 2013 51st Annual Allerton Conference on Communication, Control, and Computing (Allerton)
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
Citation
Polyanskiy, Yury. “On Dispersion of Compound DMCs.” 2013 51st Annual Allerton Conference on Communication, Control, and Computing (Allerton) (October 2013).
Version
Author's final manuscript
Abstract
Code for a compound discrete memoryless channel (DMC) is required to have small probability of error regardless of which channel in the collection perturbs the codewords. Capacity of the compound DMC has been derived classically: it equals the maximum (over input distributions) of the minimal (over channels in the collection) mutual information. In this paper the expression for the channel dispersion of the compound DMC is derived under certain regularity assumptions on the channel. Interestingly, dispersion is found to depend on a subtle interaction between the channels encoded in the geometric arrangement of the gradients of their mutual informations. It is also shown that the third-order term need not be logarithmic (unlike single-state DMCs). By a natural equivalence with compound DMC, all results (dispersion and bounds) carry over verbatim to a common message broadcast channel.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1109/Allerton.2013.6736501
