NDLI: Sufficiently myopic adversaries are blind

Content Provider	IEEE Xplore Digital Library
Author	Dey, B.K. Jaggi, S. Langberg, M.
Copyright Year	2015
Description	Author affiliation: CUHK, China (Jaggi, S.) \|\| SUNY at Buffalo, Buffalo, NY, USA (Langberg, M.) \|\| IIT Bombay, Mumbai, India (Dey, B.K.)
Abstract	In this work we consider the communication setting in which a sender, Alice, wishes to communicate with a receiver, Bob, over a channel controlled by an adversarial entity, Calvin, who is myopic. Roughly speaking, for blocklength n, the codeword $X^{n}$ transmitted by Alice is corrupted by Calvin who must base his adversarial decisions, on which characters of $X^{n}$ to corrupt and how to corrupt them, not on the entire view of the codeword $X^{n}$ but on $Z^{n},$ the image of $X^{n}$ through a noisy memoryless channel. More specifically, our communication model may be described by two channels. A memoryless channel p(z\|x) from Alice to Calvin, and an arbitrarily varying channel from Alice to Bob, p(y\|x, s) governed by a states $S^{n}$ determined by Calvin. In standard adversarial channels, the states $S^{n}$ may depend on the codeword $X^{n},$ however in our setting $S^{n}$ depends only on Calvin's view $Z^{n}.$ The myopic channel captures a broad range of channels and bridges between the standard models of memoryless and adversarial (zero error) channels. In this work we present upper and lower bounds on the capacity of myopic channels. For a number of special cases of interest we show that our bounds are tight. We extend our results to the setting of secure communication in which we require that the transmitted message remain secret from Calvin. For example, we show that if (i) Calvin may flip at most a p fraction of the bits communicated between Alice and Bob, and (ii) Calvin views $X^{n}$ through a binary symmetric channel with parameter q, then once Calvin is “sufficiently myopic” (in this case, when q > p), then the optimal communication rate is that of an adversary who is “blind” (that is, an adversary that does not see $X^{n}$ at all), which is 1-H(p) for standard communication, and H(q)-H(p) for secure communication. A similar phenomena exists for our general model of communication.
Starting Page	1164
Ending Page	1168
File Size	571202
Page Count	5
File Format	PDF
ISSN	21578117
e-ISBN	9781467377041
DOI	10.1109/ISIT.2015.7282638
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2015-06-14
Publisher Place	China
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Tin Zinc Decoding Encoding Channel capacity Memoryless systems Information Theoretic Secrecy Arbitrarily Varying Channels Myopic Jamming
Content Type	Text
Resource Type	Article

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4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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