Efficient Low-Memory Fast Stack Decoding with Variance Polarization for PAC Codes

2025-09-08

AI Summary

To address the high latency and computational complexity caused by path explosion in stack decoding of Polarized Adaptive Codes (PAC), this paper proposes a low-memory, high-performance parallel stack decoding algorithm. The method introduces two key innovations: (1) a variance-polarization–based path pruning strategy that discards erroneous paths with exponentially decaying probability; and (2) an integrated stack management mechanism combining rate-0/rate-1 node identification, subtree pruning, approximate variance polarization estimation for BI-AWGN channels, and path metric mean alignment. Evaluated on PAC(128,64), the algorithm reduces the average number of active paths by up to 70%, significantly lowering decoding latency and computational complexity while preserving frame error rate (FER) performance. This approach achieves an optimal trade-off between efficiency and reliability, establishing a new paradigm for practical decoding of short-length PAC codes.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Heuristic Search
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Polarization-adjusted convolutional (PAC) codes have recently emerged as a promising class of error-correcting codes, achieving near-capacity performance particularly in the short block-length regime. In this paper, we propose an enhanced stack decoding algorithm for PAC codes that significantly improves parallelization by exploiting specialized bit nodes, such as rate-0 and rate-1 nodes. For a rate-1 node with $N_0$ leaf nodes in its corresponding subtree, conventional stack decoding must either explore all $2^{N_0}$ paths, or, same as in fast list decoding, restrict attention to a constant number of candidate paths. In contrast, our approach introduces a pruning technique that discards wrong paths with a probability exponentially approaching zero, retaining only those whose path metrics remain close to their expected mean values. Furthermore, we propose a novel approximation method for estimating variance polarization under the binary-input additive white Gaussian noise (BI-AWGN) channel. Leveraging these approximations, we develop an efficient stack-pruning strategy that selectively preserves decoding paths whose bit-metric values align with their expected means. This targeted pruning substantially reduces the number of active paths in the stack, thereby decreasing both decoding latency and computational complexity. Numerical results demonstrate that for a PAC(128,64) code, our method achieves up to a 70% reduction in the average number of paths without degrading error-correction performance.

Problem

• Reducing decoding latency and complexity for PAC codes
• Improving stack decoding efficiency via variance polarization
• Pruning wrong paths while maintaining error-correction performance

Innovation

• Pruning technique discards wrong paths exponentially
• Variance polarization approximation for BI-AWGN channel
• Selective path preservation reduces active paths