TY - GEN

T1 - Quadratically Constrained Channels with Causal Adversaries

AU - Li, Tongxin

AU - Dey, Bikash Kumar

AU - Jaggi, Sidharth

AU - Langberg, Michael

AU - Sarwate, Anand D.

N1 - Funding Information:
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.
Funding Information:
ACKNOWLEDGMENT 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.

PY - 2018/8/15

Y1 - 2018/8/15

N2 - 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.

AB - 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.

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U2 - 10.1109/ISIT.2018.8437839

DO - 10.1109/ISIT.2018.8437839

M3 - Conference contribution

AN - SCOPUS:85052458282

SN - 9781538647806

T3 - IEEE International Symposium on Information Theory - Proceedings

SP - 621

EP - 625

BT - 2018 IEEE International Symposium on Information Theory, ISIT 2018

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2018 IEEE International Symposium on Information Theory, ISIT 2018

Y2 - 17 June 2018 through 22 June 2018

ER -