Optimal jamming Over additive noise: Vector source-channel case
This paper extends the recent analysis of optimal zero-delay jamming problem, specialized to scalar sources over scalar additive noise channels, to vector spaces. Particularly, we find the saddle point solution to the jamming problem in “vector spaces”, within its most general, non-Gaussian setting; the problem has been open even for the important special case of Gaussian source and channel. Similar to the scalar setting, linearity conditions for encoding and decoding mappings play a pivotal role in jamming, in the sense that the optimal jamming strategy is to effectively force both transmitter and receiver to default to linear mappings, i.e., the jammer ensures, whenever possible, that the transmitter and receiver cannot benefit from non-linear strategies. The optimal strategy is then “randomized” linear encoding for transmitter and generating independent noise for the jamming. Moreover, the optimal jammer allocates power according to the well-known “water-filling” over the eigenvalues of the channel noise, and the density of the jamming noise that render the optimal encoding and decoding mappings linear, is determined by the power constraints and the source density.