Secure Block Joint Source-Channel Coding with Sequential Encoding

We extend the results of Ghourchian et al. [1] to joint source-channel coding with eavesdropping. Our work characterizes the sequential encoding process using the cumulative rate distribution functions (CRDF) and includes a security constraint using the cumulative leakage distribution functions (CLF). The information leakage is defined based on the mutual information between the source and the output of the wiretap channel to the eavesdropper. We derive inner and outer bounds on the achievable CRDF for a given source and CLF, and show that the bounds are tight when the distribution achieving the capacity of the wiretap channel is the same as the one achieving the capacity of the channel.

I. Introduction

This work deals with a joint source-channel coding problem where an independent and identically distributed (IID) source is transmitted through a wiretap channel. The decoder provides a lossy reconstruction with an additive distortion constraint while the eavesdropper receives a noisy version of the codeword. The eavesdropper sequentially observes the transmitted sub-blocks. Security constraints prevent the sequential encoding from revealing too much information about the part of the source that has been transmitted so far. Since the encoding process occurs in sequential sub-blocks, the security constraints are required to avoid information about the source from being revealed early. Likewise [1], the goal is to determine achievable source-channel coding with a specified fidelity and practical applications include communication between vehicles and a central processing node in a sensor network. The information leakage constraint, represented by a cumulative rate leakage function (CLF; see Definition 3), is motivated by scenarios where there is an eavesdropper listening to the messages or information should only be revealed according to specific patterns. Our paper extends the work in [1] by considering the joint source-channel coding problem in a wiretap channel setting.