|Symmetrizability for Myopic AVCs
|Amitalok Jayant Budkuley, Indian Institute of Technology Kharagpur, India; Bikash Kumar Dey, Indian Institute of Technology Bombay, India; Sidharth Jaggi, The Chinese University of Hong Kong, China; Michael Langberg, State University of New York at Buffalo, United States; Anand D. Sarwate, Rutgers The State University of New Jersey, United States; Carol Wang, Independent Researcher, United States
|S.4: Channels with State
|Click here to download the manuscript
|Click here to watch in the Virtual Symposium
|Myopic arbitrarily varying channels (AVCs) are point-to-point communication models in which a channel state is controlled by a malicious adversary (a jammer) who receives side-information about the transmitted codeword via a side (wiretapping) channel and wishes to maximize the probability of error. They can potentially use the side information to launch a more effective attack, lowering the capacity of the channel. In this paper we provide a necessary and sufficient condition for the capacity to be zero which we call myopic symmetrizability, with a novel code construction that shows that a positive rate is achievable when the channel is not myopically symmetrizable. We also state a combinatorial conjecture, interesting in its own right, about a matching rate converse. Two examples illustrate novel phenomena in the myopic AVC: one example shows that ``codebook'' symmetrization attacks can sometimes outperform the pairwise-codeword symmetrization common in the literature, and the other shows that on occasion independent but not identically distributed code ensembles can achieve positive rate, while independent and identically distributed (i.i.d.) code constructions cannot attain positive rates.