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Codes Against Online Adversaries: Large Alphabets

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3 Author(s)
Dey, B.K. ; Dept. of Electr. Eng., Indian Inst. of Technol. Bombay, Mumbai, India ; Jaggi, S. ; Langberg, M.

In this paper, we consider the communication of information in the presence of an online adversarial jammer. In the setting under study, a sender wishes to communicate a message to a receiver by transmitting a codeword x=(x1,...,xn) symbol-by-symbol over a communication channel. The adversarial jammer can view the transmitted symbols xi one at a time and can change up to a p-fraction of them. However, for each symbol xi, the jammer's decision on whether to corrupt it or not (and on how to change it) must depend only on xj for ji. This is in contrast to the “classical” adversarial jammer which may base its decisions on its complete knowledge of x. More generally, for a delay parameter δ ∈ (0,1), we study the scenario in which the jammer's decision on the corruption of xi must depend solely on xj for jin. In this study, the transmitted symbols are assumed to be over a sufficiently large field F. The sender and receiver do not share resources such as common randomness (though the sender is allowed to use stochastic encoding). We present a tight characterization of the amount of information one can transmit in both the 0-delay and, more generally, the δ-delay online setting. We show that for 0-delay adversaries, the achievable rate asymptotically equals that of the classical adversarial model. For positive values of δ, we consider two types of jamming: additive and overwrite. We also extend our results to a jam-or-listen online model, where the online adversary can either jam a symbol or eavesdrop on it. We present computationally efficient achievability schemes even against computationally unrestricted jammers.

Published in:

Information Theory, IEEE Transactions on  (Volume:59 ,  Issue: 6 )

Date of Publication:

June 2013

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