The Capacity of Causal Adversarial Channels

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We characterize the capacity for the discrete-time arbitrarily varying channel with discrete inputs, outputs, and states when (a) the encoder and decoder do not share common randomness, (b) the input and state are subject to cost constraints, (c) the transition matrix of the channel is deterministic given the state, and (d) at each time step the adversary can only observe the current and past channel inputs when choosing the state at that time. The achievable strategy involves stochastic encoding together with list decoding and a disambiguation step. The converse uses a two-phase babble-and-push strategy where the adversary chooses the state randomly in the first phase, list decodes the output, and then chooses state inputs to symmetrize the channel in the second phase. These results generalize prior work on specific channels models (additive, erasure) to general discrete alphabets and models. Joint work with Yihan Zhang, Sidharth Jaggi, Michael Langberg, Anand D. Sarwate.

Prof. Sidharth Jaggi, School of Mathematics, University of Bristol.

Sidharth (Sid) Jaggi received his B. Tech. from I.I.T. Bombay 2000, his M.S. and Ph.D. degrees from CalTech in 2001 and 2006 respectively, all in EE. He spent 2006 as a Postdoctoral Associate at LIDS MIT. He joined the Department of Information Engineering at the Chinese University of Hong Kong in 2007, and the School of Mathematics at the University of Bristol in 2020. His interests lie at the intersection of network information theory, coding theory, and algorithms. His research group thus (somewhat unwillingly) calls itself the CAN-DO-IT team (Codes, Algorithms, Networks, Design and Optimization for Information Theory). Examples of topics he has dabbled in include network coding, sparse recovery/group-testing, covert communication, and his current obsession with adversarial channels.