Securing Distributed Function Approximation via Coding for Continuous Compound Channels
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We revisit the problem of distributed approximation of functions over multiple-access channels. Contrary to previous works, however, we do not consider the approximation problem itself, but instead we propose a method of incorporating security constraints into a class of approximation schemes to protect against passive eavesdropping. We specifically consider a scenario in which the jamming signal is stronger for the legitimate receiver than it is for the eavesdropper, and we show that in this case jamming techniques are feasible in the sense that they can deteriorate the eavesdropper's signal while not affecting the usefulness of the legitimate receiver's signal. Key ingredients for our scheme are channel resolvability as well as a newly proven result for coding for compound channels with continuous alphabets which is more general than similar results from prior works and may thus be of independent interest.
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