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.
http://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.

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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. | ||||||||||||

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Record Number: | CaltechAUTHORS:20181126-150523930 | ||||||||||||

Persistent URL: | http://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: | 27 Nov 2018 18:01 |

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