2018/05/08 by Tongxin Li, Bikash Kumar Dey, Li, Tongxin +7
Biochemistry, Genetics and Molecular Biology · Computer Science · Engineering · Mathematics · #Cooperative Communication and Network Coding #DNA and Biological Computing #FOS: Computer and information sciences #Information Theory (cs.IT) #Wireless Communication Security Techniques #cs.IT #math.IT
paper · pdf · doi:10.48550/arxiv.1805.03319
80 pages, ISIT 2018
arxiv created 2018/05/08 · openalex publication_date 2018/05/08 · arxiv updated 2018/05/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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=x1,...,xn through a communication channel. Alice and Bob do not share common randomness. Knowing Alice's encoding strategy, an adversarial jammer James chooses a real-valued length-n noise sequence s=s1,..,sn in a causal manner, i.e., each st (1<=t<=n) can only depend on x1,...,xt. Bob receives y, the sum 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. In this work, we characterize the channel capacity for such a channel as the limit superior of the optimal values of a series of optimizations. Upper and lower bounds on the optimal values 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.