Quadratically Constrained Channels with Causal Adversaries

Tongxin Li, Bikash Kumar Dey, Sidharth Jaggi, Michael Langberg, Anand D. Sarwate

Research output: Chapter in Book/Report/Conference proceedingConference contribution

5 Scopus citations


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 mathbf x=(x- 1, ldots, 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 mathbf s=(s- 1, ldots, s- n) in a causal manner: each s- t (1leq tleq n) can only depend on (x- 1, ldots, x- t). Bob receives y, the sum (over mathbb 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 sum- t=1 nx- t 2leq nP and sum- t=1 n s- t 2leq nN. In this work, we characterize the channel capacity for such a channel as the limit superior of the optimal values C- nleft(frac P Nright) of a series of optimizations. Upper and lower bounds on C- nleft(frac P Nright) 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.

Original languageEnglish (US)
Title of host publication2018 IEEE International Symposium on Information Theory, ISIT 2018
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages5
ISBN (Print)9781538647806
StatePublished - Aug 15 2018
Event2018 IEEE International Symposium on Information Theory, ISIT 2018 - Vail, United States
Duration: Jun 17 2018Jun 22 2018

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
ISSN (Print)2157-8095


Other2018 IEEE International Symposium on Information Theory, ISIT 2018
Country/TerritoryUnited States

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Information Systems
  • Modeling and Simulation
  • Applied Mathematics


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