Polar code decoding improved with offline variance perturbation design
Parallel Successive Cancellation Perturbation-Enhanced Decoding of Polar Codes via Offline Variance Design
Information Theory
Summary
Polar codes help protect data sent over noisy communication channels. The authors show a new way to improve decoding these codes by preparing all the trial corrections ahead of time instead of waiting for previous attempts. This approach lets the decoder try several possibilities in parallel, making it faster and more effective, especially for shorter messages. Their method uses math to pick the best variations before decoding starts, which reduces errors when decoding data.
What this means in practice
- •For telecommunication engineers: Improve error correction in wireless systems by using pre-designed parallel perturbations to decode polar codes faster and more reliably.
- •For embedded system developers: Implement low-latency decoding of polar codes in hardware with offline variance parameters allowing simultaneous processing branches.
Authors
Changwei Tu, Xuanyu Li, Kai Niu
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.