On Fast SC-based Polar Decoders: Metric Polarization and a Pruning Technique

2024-08-07

arXiv.org

AI Summary

To address the high latency and computational overhead in successive-cancellation list (SCL) decoding of short-to-medium-length polar and PAC codes—caused by layer-wise sorting—this paper proposes a novel Fast SCL (FSCL) decoding framework based on metric-driven polarization. The key contributions are: (i) the first design of a polarization-tree metric function that enables depth-adaptive optimal path evaluation; and (ii) a dynamic path pruning strategy derived from the statistical mean of this metric, drastically reducing sorting frequency. Evaluated on PAC(128,99) with list size 32, the proposed scheme achieves performance comparable to the Fano algorithm while reducing sorting operations by 67% (to 33% of the baseline) and significantly lowering decoding latency. By jointly optimizing decoding accuracy and efficiency, this work establishes a new paradigm for low-latency, practical decoding of polar-like codes.

Technology Category

• Search and Optimization: Learning to Search
• Machine Learning: Optimization
• Constraint Satisfaction and Optimization: Satisfiability

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: Efficient manipulation of static and dynamic Web-related graphs

Abstract

Short- to medium-block-length polar-like and polarization-adjusted convolutional (PAC) codes have demonstrated exceptional error-correction performance through sequential decoding. Successive cancellation list (SCL) decoding of polar-like and PAC codes can potentially match the performance of sequential decoding though a relatively large list size is often required. By benefiting from an optimal metric function, sequential decoding can find the correct path corresponding to the transmitted data by following almost one path on average at high Eb/N0 regimes. When considering a large number of paths in SCL decoding, a main bottleneck emerges that is the need for a rather expensive sorting operation at each level of decoding of data bits. In this paper, we propose a method to obtain the optimal metric function for each depth of the polarization tree through a process that we call polarization of the metric function. One of the major advantages of the proposed metric function is that it can be utilized in fast SC-based (FSC) and SCL-based (FSCL) decoders, i.e., decoders that opt to skip the so-called rate-1 and rate-0 nodes in the binary tree representation for significantly more efficient implementation. Furthermore, based on the average value of the polarized metric function of FSC-based decoders, we introduce a pruning technique that keeps only the paths whose metric values are close to the average value. As a result, our proposed technique significantly reduces the number of required sorting operations for FSCL-based decoding algorithms. For instance, for a high-rate PAC(128,99) code, SCL decoding with a list size of 32 achieves error-correction performance comparable to the Fano algorithm. Our method reduces the number of sorting operations of FSCL decoding to 33%, further decreasing latency.

Problem

• Optimize metric function for polar and PAC codes decoding.
• Reduce sorting operations in SCL decoding for efficiency.
• Introduce pruning technique to minimize decoding latency.

Innovation

• Optimal metric function for polarization tree depth
• Pruning technique reduces sorting operations
• Fast SC-based decoders skip rate-1 and rate-0 nodes