Polar and Convolutional Codes for the Unequal Message Protection Problem

2026-04-20

AI Summary

This work addresses the rate loss and spectral efficiency challenges in unequal message protection (UMP) at short blocklengths by proposing a general framework that achieves high-efficiency UMP without requiring customized code design. The approach combines polar codes with convolutional coset codes and employs a two-stage decoding strategy: first, a computable approximation of likelihood ratio tests identifies mutually exclusive message classes; second, maximum (or approximate) likelihood decoding is performed within each class, augmented by CRC for enhanced reliability. The proposed scheme closely approaches theoretical bounds at finite blocklengths, matching the performance of existing specialized polar-code-based UMP methods while simultaneously offering robustness and high spectral efficiency.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Multiagent Systems: Multiagent Systems under Uncertainty
• Reasoning under Uncertainty: Sequential Decision Making

Application Category

• Security and Privacy: Large-scale security measurements
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

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.

Problem

• unequal message protection
• short blocklength
• rate loss
• preamble-based solutions
• message class disjointness

Innovation

• unequal message protection
• polar codes
• convolutional codes
• two-step decoding
• short blocklength