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Quadratically Constrained Channels with Causal Adversaries

Li, Tongxin and Dey, Bikash Kumar and Jaggi, Sidharth and Langberg, Michael and Sarwate, Anand D. (2018) Quadratically Constrained Channels with Causal Adversaries. In: 2018 IEEE International Symposium on Information Theory (ISIT). IEEE , Piscataway, NJ, pp. 621-625. ISBN 978-1-5386-4780-6. https://resolver.caltech.edu/CaltechAUTHORS:20181126-150523930

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Abstract

We consider the problem of communication over a channel with a causal jamming adversary subject to quadratic constraints. A sender Alice wishes to communicate a message to a receiver Bob by transmitting a real-valued length-n codeword x=(x_1, ..., x_n) through a communication channel. Alice and Bob do not share common randomness. Knowing Alice's encoding strategy, a jammer James chooses a real-valued length- n adversarial noise sequence s=(s_1, ..., s_n) in a causal manner: each s_t (1 ≤ t ≤ n) can only depend on (x_1, ..., x_t). Bob receives y, the sum (over R) of Alice's transmission x and James' jamming vector s, and is required to reliably estimate Alice's message from this sum. In addition, Alice and James's transmission powers are restricted by quadratic constraints P > 0 and N > 0 such that Σ_(t=1)^n x_t^2 ≤ nP and Σ_(t=1)^n s_t^2 ≤ nN. In this work, we characterize the channel capacity for such a channel as the limit superior of the optimal values C_n([P/N]) of a series of optimizations. Upper and lower bounds on C_n([P/N]) are provided both analytically and numerically. Interestingly, unlike many communication problems, in this causal setting Alice's optimal codebook may not have a uniform power allocation - for certain SNR a codebook with a two-level uniform power allocation results in a strictly higher rate than a codebook with a uniform power allocation would.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
https://doi.org/10.1109/ISIT.2018.8437839DOIArticle
ORCID:
AuthorORCID
Sarwate, Anand D.0000-0001-6123-5282
Additional Information:© 2018 IEEE. This work was partially funded by a grant from the University Grants Committee of the Hong Kong Special Administrative Region (Project No. AoE/E-02/08), RGC GRF grants 14208315 and 14313116, NSF grant 1526771, and a grant from Bharti Centre for Communication in IIT Bombay.
Funders:
Funding AgencyGrant Number
University Grants Committee of the Hong Kong Special Administrative RegionAoE/E-02/08
Research Grants Council (RGC) of Hong Kong14208315
Research Grants Council (RGC) of Hong Kong14313116
NSFCCF-1526771
India Institute of TechnologyUNSPECIFIED
Record Number:CaltechAUTHORS:20181126-150523930
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20181126-150523930
Official Citation:T. Li, B. K. Dey, S. Jaggi, M. Langberg and A. D. Sarwate, "Quadratically Constrained Channels with Causal Adversaries," 2018 IEEE International Symposium on Information Theory (ISIT), Vail, CO, 2018, pp. 621-625. doi: 10.1109/ISIT.2018.8437839
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:91193
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:27 Nov 2018 18:01
Last Modified:03 Oct 2019 20:32

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