Polar Coding for Fading Channels

TL;DR

This paper introduces a hierarchical polar coding scheme for Gaussian fading channels with BPSK modulation, enabling capacity achievement without requiring instantaneous channel state information at the transmitter.

Contribution

A novel polar coding scheme that adapts to fading channels by modeling polarization over blocks, achieving capacity without instantaneous channel state information.

Findings

Achieves capacity of fading BSC without CSI at transmitter

Models polarization as binary erasure channels over fading blocks

Utilizes hierarchical polar coding for variable channel states

Abstract

A polar coding scheme for fading channels is proposed in this paper. More specifically, the focus is Gaussian fading channel with a BPSK modulation technique, where the equivalent channel could be modeled as a binary symmetric channel with varying cross-over probabilities. To deal with variable channel states, a coding scheme of hierarchically utilizing polar codes is proposed. In particular, by observing the polarization of different binary symmetric channels over different fading blocks, each channel use corresponding to a different polarization is modeled as a binary erasure channel such that polar codes could be adopted to encode over blocks. It is shown that the proposed coding scheme, without instantaneous channel state information at the transmitter, achieves the capacity of the corresponding fading binary symmetric channel, which is constructed from the underlying fading AWGN channel through the modulation scheme.