Polar and Convolutional Codes for the Unequal Message Protection Problem

TL;DR

This paper introduces polar and convolutional coset codes tailored for unequal message protection in short blocklengths, offering a rate-efficient alternative to preamble-based methods.

Contribution

It presents a novel two-step decoding architecture and conditions for message class disjointness, improving finite-length performance in UMP scenarios.

Findings

Polar and convolutional coset codes perform comparably to existing methods.

The proposed approach reduces rate loss in short blocklength regimes.

Numerical results confirm robustness and spectral efficiency.

Abstract

This paper proposes the design of polar and convolutional coset codes for the unequal message protection (UMP) in the short blocklength regime, to overcome the rate loss introduced by preamble-based solutions. After providing conditions to ensure message class disjointness, a two-step decoding architecture is proposed: it first identifies the message class via a likelihood ratio test--computable exactly for convolutional codes and approximated for polar codes--and subsequently performs maximum (or near) likelihood decoding among the codewords of the chosen message class. Numerical results show that our construction closely tracks finite-length benchmarks. Specifically, the analyzed CRC-aided polar codes perform comparable to existing polar code approaches, without requiring specific code design, while offering a robust and spectrally efficient solution for UMP scenarios.