Abstract
In this paper, we determine the capacity of the Gaussian arbitrarily-varying channel with a (possibly stochastic) encoder and a deterministic list-decoder under the average probability of error criterion. We assume that both the legitimate and the adversarial signals are restricted by their power constraints. We also assume that there is no path between the adversary and the legitimate user but the adversary knows the legitimate user’s code. We show that for any list size L, the capacity is equivalent to the capacity of a point-to-point Gaussian channel with noise variance increased by the adversary power, if the adversary has less power than L times the transmitter power; otherwise, the capacity is zero. In the converse proof, we show that if the adversary has enough power, then the decoder can be confounded by the adversarial superposition of several codewords while satisfying its power constraint with positive probability. The achievability proof benefits from a novel variant of the Csiszár-Narayan method for the arbitrarily-varying channel.
Highlights
An arbitrarily-varying channel (AVC) represents a memoryless channel including unknown parameters that are changing arbitrarily from channel use to channel use
The capacity of the AVC depends on the coding method, the performance criterion and the amount of adversary’s knowledge about the transmitted signal
The second part of Csiszár and Narayan work in Reference [6] focuses on the deterministic code capacity of AVC under input and state constraints for the same performance criterion
Summary
An arbitrarily-varying channel (AVC) represents a memoryless channel including unknown parameters that are changing arbitrarily from channel use to channel use. The second part of Csiszár and Narayan work in Reference [6] focuses on the deterministic code capacity of AVC under input and state constraints for the same performance criterion They proved that in this case if the capacity is positive it is less than or equal to the corresponding random code capacity. The authors in Reference [20] extended the list-decoding result to the discrete-memoryless AVCs with state constraints They determined upper and lower bounds on the capacity by introducing two notions of symmetrizability for this channel. Under the average probability of error criterion and without common randomness, we obtain the capacity of GAVC with list decoding to be equal to the corresponding randomized code capacity if the list size is greater than the power ratio of the jammer to the legitimate user; otherwise, the capacity is zero.
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