Hierarchical Polar Coding for Achieving Secrecy over Fading Wiretap Channels without any Instantaneous CSI

TL;DR

This paper introduces a hierarchical polar coding scheme that achieves secrecy over fading wiretap channels without requiring instantaneous CSI at the transmitter, effectively reaching the secrecy capacity in various fading scenarios.

Contribution

A novel hierarchical polar coding scheme is proposed that attains secrecy capacity without instantaneous CSI, expanding secure communication capabilities over fading channels.

Findings

Achieves secrecy capacity in simultaneous fading scenarios.

No increase in secrecy capacity with instantaneous CSI in certain cases.

Provides bounds and analysis for different fading conditions.

Abstract

This paper presents a polar coding scheme to achieve secrecy in block fading binary symmetric wiretap channels without the knowledge of instantaneous channel state information (CSI) at the transmitter. For this model, a coding scheme that hierarchically utilizes polar codes is presented. In particular, on polarization of different binary symmetric channels over different fading blocks, each channel use is modeled as an appropriate binary erasure channel over fading blocks. Polar codes are constructed for both coding over channel uses for each fading block and coding over fading blocks for certain channel uses. In order to guarantee security, random bits are introduced at appropriate places to exhaust the observations of the eavesdropper. It is shown that this coding scheme, without instantaneous CSI at the transmitter, is secrecy capacity achieving for the simultaneous fading scenario. For the independent fading case, the capacity is achieved when the fading realizations for the eavesdropper channel is always degraded with respect to the receiver. For the remaining cases, the gap is analyzed by comparing lower and upper bounds. Remarkably, for the scenarios where the secrecy capacity is achieved, the results imply that instantaneous CSI does not increase the secrecy capacity.