Polar Coding for Block Fading Channels

TL;DR

This paper develops polar coding schemes for block fading channels, including scenarios with and without receiver CSI, achieving ergodic capacity by decomposing channels and employing interleaving for improved finite-length performance.

Contribution

It introduces a capacity-preserving decomposition of block fading channels into sub-channels and designs polar codes for each, with enhancements for finite-length performance using interleaving.

Findings

Achieves ergodic capacity under various CSI conditions.

Decomposes block fading channels into sub-channels for polar coding.

Uses interleaving to improve finite-length performance.

Abstract

In this paper, we consider the problem of polar coding for block fading channels, with emphasis on those with instantaneous channel state information (CSI) at neither the transmitter nor the receiver. Our approach is to decompose a block fading channel of $T_c$ symbols per coherent interval into $T_c$ binary-input sub-channels in a capacity-preserving way, and design a polar code for each of them. For the case when instantaneous CSI is available at the receiver, a random interleaver can be used to enable joint encoding and decoding of all sub-channels so as to enhance the finite length performance. It is shown that our proposed schemes achieve the ergodic capacity of binary-input block fading channels under various CSI assumptions.