An Error Correction Technique for Product Codes Construction of PAC Codes

Abstract

High-rate product codes are widely employed in modern high-speed communication systems, and their performance is heavily dependent on their component codes. While polar codes are theoretically capacity-achieving, their error-correction performance degrades significantly at the finite blocklengths typical of product code applications. To address this limitation, we propose a novel product code construction based on Polarization-Adjusted Convolutional (PAC) codes, referred to as PAC product codes (PAC-PCs). Additionally, we design an improved two-step decoder for PAC-PC, which incorporates an effective error-localization strategy and an error-pattern matching mechanism to resolve complex decoding ambiguities. Furthermore, the decoder employs an adaptive early termination technique to reduce decoding latency and computational complexity, particularly at high signal-to-noise ratio (SNR), thereby improving energy efficiency. Simulation results demonstrate that the proposed PAC-PC significantly outperforms conventional polar product codes (Polar-PCs) in terms of error-correction performance. Compared to established iterative product codes and staircase codes, the proposed PAC-PC achieves a favorable trade-off between error-correction performance and complexity.