On Secure One-Helper Source Coding With Action-Dependent Side Information

In this article, we consider a secure one-helper distributed source coding system, with action-dependent side information. Specifically, the main encoder observes an independent and identically distributed (i.i.d.) source X n and wishes to compress this source to the decoder. The helper compresses the correlated source Y-n to the decoder. The eavesdropper, having access to the information bits sent by the main encoder, can observe side information Z(n) as well. Besides, side information Z(n) and correlated source Y-n can be influenced by a cost-constrained action sequence taken by the decoder. This class of problems can be seen as an nontrivial extension of the secure one-helper source coding with additional cost-constrained actions. The purpose of this article is to study the impact of the helper on achievable ratedistortion-cost-leakage. An inner bound of the achievable ratedistortion-cost-leakage is provided for the discrete memoryless setting. This inner bound is further shown to be tight when Y-n is required to be reconstructed losslessly, and equivalent to the inner bound of Villard et al. when there is no action taken at the decoder. Numerical examples on binary symmetric sources are also discussed in this article.