Changwei Tu

Changwei Tu, Yang Liu, Xianzhao Feng et al.

Blind recognition of polar codes remains challenging in non-cooperative scenarios, particularly for information-set recognition with known code length. Existing methods mainly rely on threshold decisions determined by the generator-matrix structure and channel bit error probability, without fully exploiting the soft information in received signals. In this letter, we propose a blind recognition method using successive cancellation list (SCL) decoding for polar codes with known code length. The proposed method exploits the distinct statistical behaviors of frozen and information bits in source-side decision log-likelihood ratios (LLRs) over multiple received vectors: frozen bits tend to favor zero decisions, whereas information bits exhibit nearly equiprobable $0/1$ decisions. Based on this property, the decoder expands candidate paths under the frozen-bit and information-bit hypotheses at each bit position, evaluates their reliabilities using the corresponding average path metrics, and retains only the $L_{\mathrm{list}}$ most reliable paths for subsequent recognition. Finally, the information-set pattern corresponding to the most reliable surviving path is selected as the recognition result. Simulation results show that the proposed scheme improves the recognition success rate as the list size increases. For the $(32,16)$, $(64,32)$, and $(128,64)$ polar codes, it achieves at least $2.5$ dB gain over the previous method when $L_{\mathrm{list}}=64$.

Hengrong Du, Qi Feng, Changwei Tu et al.

We consider the constrained sampling problem where the goal is to sample from a target distribution on a constrained domain. We propose skew-reflected non-reversible Langevin dynamics (SRNLD), a continuous-time stochastic differential equation with skew-reflected boundary. We obtain non-asymptotic convergence rate of SRNLD to the target distribution in both total variation and 1-Wasserstein distances. By breaking reversibility, we show that the convergence is faster than the special case of the reversible dynamics. Based on the discretization of SRNLD, we propose skew-reflected non-reversible Langevin Monte Carlo (SRNLMC), and obtain non-asymptotic discretization error from SRNLD, and convergence guarantees to the target distribution in 1-Wasserstein distance. We show better performance guarantees than the projected Langevin Monte Carlo in the literature that is based on the reversible dynamics. Numerical experiments are provided for both synthetic and real datasets to show efficiency of the proposed algorithms.

Yingli Wang, Changwei Tu, Xiaoyu Wang et al.

The problem of sampling a target probability distribution on a constrained domain arises in many applications including machine learning. For constrained sampling, various Langevin algorithms such as projected Langevin Monte Carlo (PLMC) based on the discretization of reflected Langevin dynamics (RLD) and more generally skew-reflected non-reversible Langevin Monte Carlo (SRNLMC) based on the discretization of skew-reflected non-reversible Langevin dynamics (SRNLD) have been proposed and studied in the literature. This work focuses on the long-time behavior of SRNLD, where a skew-symmetric matrix is added to RLD. Although acceleration for SRNLD has been studied, it is not clear how one should design the skew-symmetric matrix in the dynamics to achieve good performance in practice. We establish a large deviation principle (LDP) for the empirical measure of SRNLD when the skew-symmetric matrix is chosen such that its product with the inward unit normal vector field on the boundary is zero. By explicitly characterizing the rate functions, we show that this choice of the skew-symmetric matrix accelerates the convergence to the target distribution compared to RLD and reduces the asymptotic variance. Numerical experiments for SRNLMC based on the proposed skew-symmetric matrix show superior performance, which validate the theoretical findings from the large deviations theory.