Secure Block Source Coding with Sequential Encoding

TL;DR

This paper establishes fundamental bounds on sequential source coding rates with security constraints, introducing new concepts like CRDF and CLF, and characterizes optimal rate distributions using majorization theory.

Contribution

It introduces the concepts of CRDF and CLF for sequential encoding with security, providing necessary and sufficient conditions for achievable rate distributions.

Findings

Concave-hull of CRDF characterizes optimal rate distribution.

Derived bounds for secure sequential source coding.

Established conditions for achievable CRDF and CLF.

Abstract

We introduce fundamental bounds on achievable cumulative rate distribution functions (CRDF) to characterize a sequential encoding process that ensures lossless or lossy reconstruction subject to an average distortion criterion using a non-causal decoder. The CRDF describes the rate resources spent sequentially to compress the sequence. We also include a security constraint that affects the set of achievable CRDF. The information leakage is defined sequentially based on the mutual information between the source and its compressed representation, as it evolves. To characterize the security constraints, we introduce the concept of cumulative leakage distribution functions (CLF), which determines the allowed information leakage as distributed over encoded sub-blocks. Utilizing tools from majorization theory, we derive necessary and sufficient conditions on the achievable CRDF for a given independent and identically distributed (IID) source and CLF. One primary result of this paper is that the concave-hull of the CRDF characterizes the optimal achievable rate distribution.