Secure Joint Source-Channel Coding for the AWGN Channel with Feedback: A Finite Blocklength Analysis

TL;DR

This paper investigates finite blocklength performance of secure joint source-channel coding over AWGN channels with feedback, showing classical schemes are suboptimal and proposing improved methods along with new converse bounds.

Contribution

It introduces a modified Schalkwijk-Kailath scheme for finite blocklengths and establishes the first finite blocklength converse for the AWGN wiretap channel with feedback.

Findings

Classical SK scheme is suboptimal in finite blocklengths.

Proposed modified SK scheme outperforms classical scheme.

Finite blocklength converse bounds are established.

Abstract

In the literature, it has been shown that the secrecy capacity of the additive white Gaussian noise (AWGN) wiretap channel with noise-free feedback equals the capacity of the same model without secrecy constraint, and the classical Schalkwijk-Kailath (SK) scheme achieves the secrecy capacity. In this paper, we show that in finite blocklength regime, the SK scheme is not optimal, and propose a modified SK scheme which may perform better than the classical one. Besides this, this paper establishes a finite blocklength converse for the AWGN wiretap channel with feedback, which can also be viewed as a converse for the same model without secrecy constraint. To the best of the authors' knowledge, this is the first paper to address such a problem, and the results of this paper are further explained via numerical examples.