Optimal parameter design for estimation theoretic secure broadcast

Abstract

In this letter, estimation theoretic secure broadcast of a random parameter is investigated. In the considered setting, each receiver device employs a fixed estimator and carries a certain security risk such that its decision can be available to a malicious third party with a certain probability. The encoder at the transmitter is allowed to use a random mapping to minimize the weighted sum of the conditional Bayes risks of the estimators under secrecy and average power constraints. After formulating the optimal parameter design problem, it is shown that the optimization problem can be solved individually for each parameter value and the optimal mapping at the transmitter involves a randomization among at most three different signal levels. Sufficient conditions for improvability and non-improvability of the deterministic design via stochastic encoding are obtained. Numerical examples are provided to corroborate the theoretical results.