Adaptive Perturbation Enhanced SCL Decoder for Polar Codes

TL;DR

This work addresses the diminishing gains of SCL-flip decoding for polar codes at large block lengths by introducing SCL-perturbation, which applies small perturbations to the received symbols before multiple SCL decoding attempts. The basic random perturbation provides non-diminishing gains, while an adaptive biased perturbation leverages prior decoding outcomes to bias perturbations, enabling near-double-list-size performance with only two decoding attempts. The approach yields stable gains across code lengths, rates, and list sizes, with favorable complexity and hardware implications, and shows potential for further enhancement via deep learning-based perturbation. Overall, SCL-perturbation offers a highly efficient, hardware-friendly alternative to increasing list size for polar-code decoding, maintaining performance improvements as code length grows.

Abstract

For polar codes, successive cancellation list (SCL) decoding algorithm significantly improves finite-length performance compared to SC decoding. SCL-flip decoding can further enhance the performance but the gain diminishes as code length increases, due to the difficulty in locating the first error bit position. In this work, we introduce an SCL-perturbation decoding algorithm to address this issue. A basic version of the algorithm introduces small random perturbations to the received symbols before each SCL decoding attempt, and exhibits non-diminishing gain at large block lengths. Its enhanced version adaptively performs random perturbations or directional perturbation on each received symbol according to previous decoding results, and managed to correct more errors with fewer decoding attempts. Extensive simulation results demonstrate stable gains across various code rates, lengths and list sizes. To the best of our knowledge, this is the first SCL enhancement with non-diminishing gains as code length increases, and achieves unprecedented efficiency. With only one additional SCL-$L$ decoding attempt (in total two), the proposed algorithm achieves SCL-$2L$-equivalent performance. Since the gain is obtained without increasing list size, the algorithm is best suited for hardware implementation.

Figures (18)

• Figure 1: BLER performance of SCL($8\sim16$) decoding, SCL perturbation with T = 10 decoding attempts and SCL flip with T = 10 for polar codes of $R=0.5$ and $N=\{256,1024,4096,16384\}$.
• Figure 2: BLER performance of SCL ($8\sim16$) decoding, SCL-perturbation (random and bias) with T = 2 decoding attempt for polar codes of $R=0.5$ and $N=\{256,1024,4096,16384\}$.
• Figure 3: The algorithm applies biased perturbation only to the all-disagreed bits.
• Figure 4: The optimal perturbation powers vary slightly at different SNRs.
• Figure 5: BLER performance for polar codes of $R=\frac{1}{4}$ and $N=\{256,1024,4096,16384\}$.