Polar Coded Repetition for Low-Capacity Channels

TL;DR

This paper introduces a novel polar coded repetition scheme that enhances low-capacity channel performance with minimal added complexity, suitable for ultra-low-power IoT applications.

Contribution

It proposes a modified polar coding method with improved asymptotic achievable rate for low-capacity channels, maintaining low complexity.

Findings

Improved asymptotic achievable rate for polar-repetition scheme.

Maintains low encoding and decoding complexity.

Analyzed performance specifically for binary erasure channels.

Abstract

Constructing efficient low-rate error-correcting codes with low-complexity encoding and decoding have become increasingly important for applications involving ultra-low-power devices such as Internet-of-Things (IoT) networks. To this end, schemes based on concatenating the state-of-the-art codes at moderate rates with repetition codes have emerged as practical solutions deployed in various standards. In this paper, we propose a novel mechanism for concatenating outer polar codes with inner repetition codes which we refer to as polar coded repetition. More specifically, we propose to transmit a slightly modified polar codeword by deviating from Arikan's standard 2 x 2 Kernel in a certain number of polarization recursions at each repetition block. We show how this modification can improve the asymptotic achievable rate of the polar-repetition scheme, while ensuring that the overall encoding and decoding complexity is kept almost the same. The achievable rate is analyzed for the binary erasure channels (BEC).