PAC Codes Meet CRC-Polar Codes

2025-01-30

AI Summary

To address the limited bit-error performance of polar codes in both short- and long-code regimes, this paper proposes the PS-PAC coding framework, which integrates CRC-aided decoding, convolutional pre-coding, and a dynamic parity masking mechanism to jointly optimize codeword weight distribution and frozen-bit design. A novel continuous-division-based dynamic parity masking technique is introduced, coupled with row-wise decomposition of the polarization transform and successive-cancellation list (SCL) decoding, enabling fine-grained frozen-bit configuration. Experimental results demonstrate a 0.5 dB SNR gain for short codes (N=128, K=64) and a 0.12 dB overall improvement for long codes (N=1024, K=512), accompanied by significant frame-error-rate reduction. The framework balances theoretical rigor with practical implementability, offering a promising solution for ultra-reliable short-packet communications.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Security and Privacy: Large-scale security measurements
• User Modeling, Personalization and Recommendation: Psychology-informed user models and recommender systems

Abstract

CRC-Polar codes under SC list decoding are well-regarded for their competitive error performance. This paper examines these codes by focusing on minimum weight codewords and breaking them down into the rows of the polar transform. Inspired by the significant impact of parity check bits and their positions, we apply a shifted rate-profile for polarization-adjusted convolutional (PS-PAC) codes, thereby achieving similar improvements in the weight distribution of polar codes through precoding. The results demonstrate a significant improvement in error performance, achieving up to a 0.5 dB power gain with short PS-PAC codes. Additionally, leveraging convolutional precoding in PAC codes, we adopt a continuous deployment (masking) of parity check bits derived from the remainder of continuous division of the partial message polynomial and the CRC polynomial over frozen positions in the rate-profile. This approach enhances performance for long codes, with an overall improvement of 0.12 dB.

Problem

• PAC codes
• CRC-polar codes
• error correction capability

Innovation

• Polarization-adjusted Convolutional Accumulation Coded (PS-PAC) Codes
• Improved Weight Distribution
• Enhanced Error Resistance