Finite-blocklength bounds for wiretap channels

This paper investigates the maximal secrecy rate over a wiretap channel subject to reliability and secrecy constraints at a given blocklength. New achievability and converse bounds are derived, which are shown to be tighter than existing bounds. The bounds also lead to the tightest second-order coding rate for discrete memoryless and Gaussian wiretap channels.

I. Introduction

We consider the problem of secure communication over a wiretap channel with a transmitter (Alice), a legitimate receiver (Bob), and an eavesdropper (Eve). The transmitter aims to communicate a message to the receiver while keeping it secret from the eavesdropper. We are interested in finding upper and lower bounds on the maximal secret communication rate for a given blocklength , error probability , and information leakage . Throughout the paper, the information leakage to the eavesdropper is measured by the total variation distance between and .