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

Abstract

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 $X^{\textit{n}}$ and wishes to compress this source to the decoder. The helper compresses the correlated source $Y^{\textit{n}}$ to the decoder. The eavesdropper, having access to the information bits sent by the main encoder, can observe side information $Z^{\textit{n}}$ as well. Besides, side information $Z^{\textit{n}}$ and correlated source $Y^{\textit{n}}$ 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 rate-distortion-cost-leakage. An inner bound of the achievable rate-distortion-cost-leakage is provided for the discrete memoryless setting. This inner bound is further shown to be tight when $Y^{\textit{n}}$ 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.