Rate-Matching Deep Polar Codes via Polar Coded Extension

2025-05-11

AI Summary

Deep polar codes are constrained by codeword lengths restricted to powers of two, limiting their applicability in practical communication systems requiring arbitrary (non-power-of-two) block lengths. To address this, we propose a novel rate-matching scheme based on polar code expansion: codewords are constructed via layer-wise concatenation of polar-encoded segments, enabling flexible, fine-grained length adaptation—introduced here for the first time in deep polar coding frameworks. We further design a hierarchical soft-output successive cancellation list (SCL) decoder and a multi-layer greedy configuration strategy to enhance decoding efficiency. A rigorous bit error probability analysis model is established to characterize performance. Compared with conventional rate-matching approaches, the proposed method achieves significant coding gain improvements—particularly at medium-to-high code rates and short block lengths—as validated by extensive simulations.

Technology Category

• Search and Optimization: Learning to Search
• Machine Learning: Deep Neural Architectures and Foundation Models
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs

Abstract

Deep polar codes are pre-transformed polar codes that employ a multi-layered polar kernel transformation strategy to enhance code performance in short blocklength regimes. However, like conventional polar codes, their block length is constrained to powers of two, as the final transformation layer uses a conventional polar kernel matrix. This paper introduces a novel rate-matching technique for deep polar codes using code extension, particularly effective when the desired code length slightly exceeds a power of two. The key idea is to exploit the layered structure of deep polar codes by concatenating polar codewords generated at each transformation layer. Based on this structure, we also develop an efficient decoding algorithm leveraging soft-output successive cancellation list decoding and provide comprehensive error probability analysis supporting our code design algorithms. Additionally, we propose a computationally efficient greedy algorithm for multi-layer configurations. Extensive simulations confirm that our approach delivers substantial coding gains over conventional rate-matching methods, especially in medium to high code-rate regimes.

Problem

• Extends deep polar codes beyond power-of-two blocklength constraints
• Enhances rate-matching via multi-layer polar codeword concatenation
• Improves decoding efficiency with soft-output successive cancellation

Innovation

• Multi-layered polar kernel transformation strategy
• Rate-matching via polar coded extension
• Efficient decoding with soft-output list decoding