Parallel Successive Cancellation Perturbation-Enhanced Decoding of Polar Codes via Offline Variance Design

2026-09-28

AI Summary

This study addresses the additional latency introduced by serial dependencies in perturbation-enhanced decoding for polar codes by proposing a parallelizable Successive Cancellation Perturbation (SCP) decoding architecture. The core methodology introduces an offline variance greedy selection algorithm based on failed-frame classification, which combines Gaussian approximation with backward recursion to design perturbation variances, thereby enabling multiple branches to initiate independently and decode in parallel. Experimental results demonstrate that, given an identical number of branches, the proposed scheme significantly reduces the block error rate. Furthermore, the performance gains become more pronounced as the code length decreases and the number of branches increases. Consequently, this approach effectively balances decoding performance and latency efficiency for short-to-medium polar codes.

Abstract

Successive cancellation perturbation-enhanced (SCP) decoding improves the performance of finite-length polar codes by performing multiple SC decoding attempts with receiver-side perturbations. However, many existing perturbation schemes generate or update subsequent perturbations according to the outcomes of previous decoding attempts, resulting in additional decoding latency. In this paper, we propose an offline variance design (OVD) method for parallel SCP (PSCP) decoding of short- and medium-length polar codes. First, we formulate the exact recovery objective conditioned on ordinary SC failure and classify failed frames by the position of the first genie-aided intrinsic error and the number of subsequent intrinsic errors. We also derive a consistent Gaussian representation of the perturbed channel that preserves min-sum SC hard decisions. Second, we construct a class-based approximation of the recovery objective using Gaussian approximation and backward recursions, accounting for both error correction and new errors introduced by perturbations. We prove that both the exact and analytical objectives are nondecreasing and exhibit diminishing marginal gains as independent branches are added. Third, we develop a greedy algorithm to select variances from a finite candidate set for a given code, signal-to-noise ratio (SNR), and number of perturbation branches. All variances are determined offline, allowing the original SC branch and all perturbation branches to start simultaneously. Simulations for rate-$1/2$ polar codes of lengths $64$, $128$, $256$, and $512$ show that OVD-PSCP achieves lower block error rates (BLERs) than conventional SCP with the same number of perturbation branches. The gains are larger for shorter codes and increase as the number of perturbation branches grows.

Problem

• Polar codes
• Successive cancellation perturbation
• Decoding latency
• Parallel decoding

Innovation

• Polar Codes
• Offline Variance Design
• Parallel Successive Cancellation Perturbation
• Greedy Algorithm
• Gaussian Approximation