极化码的并行连续消除扰动增强解码：基于离线方差设计
Parallel Successive Cancellation Perturbation-Enhanced Decoding of Polar Codes via Offline Variance Design
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- Key Laboratory of Universal Wireless Communications, Ministry of Education, Beijing University of Posts and Telecommunications（北京邮电大学通用无线通信教育部重点实验室）
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中文总结 AI 辅助
提出离线方差设计方法，为并行连续消除扰动增强解码预先确定扰动方差，在相同分支数下降低短中长极化码的块错误率。
中文摘要 AI 辅助
连续消除扰动增强（SCP）解码通过执行多次带有接收端扰动的连续消除（SC）解码尝试，改善了有限长度极化码的性能。然而，许多现有的扰动方案根据先前解码尝试的结果来生成或更新后续扰动，导致额外的解码延迟。本文针对短码和中长码极化码，提出了一种用于并行SCP（PSCP）解码的离线方差设计（OVD）方法。首先，我们以普通SC失败为条件，形式化精确恢复目标，并根据首次天才辅助内在错误的位置以及后续内在错误的数量对失败帧进行分类。我们还推导了扰动信道的一致高斯表示，该表示保留了最小和SC硬判决。其次，我们利用高斯近似和向后递推构建了恢复目标的基于类别的近似，同时考虑了纠错和扰动引入的新错误。我们证明了精确目标和分析目标都是非递减的，并且随着独立分支的添加，边际增益递减。第三，我们开发了一种贪心算法，针对给定码、信噪比（SNR）和扰动分支数量，从有限候选集中选择方差。所有方差均在离线确定，使得原始SC分支和所有扰动分支能够同时启动。对码率1/2、长度分别为64、128、256和512的极化码进行的仿真表明，在相同扰动分支数量下，OVD-PSCP实现了比传统SCP更低的块错误率（BLER）。增益在较短码上更大，并随着扰动分支数量的增加而增大。
英文摘要
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.
