Partitioned Successive-Cancellation List Flip Decoding of Polar Codes

TL;DR

The paper tackles finite-length polar-code decoding complexity by introducing Partitioned SCLF (PSCLF), which partitions the codeword and applies SCLF per partition to enable early termination. It provides a partition design guided by the SCL dynamics and a per-partition CRC structure to mitigate collision-induced errors, achieving up to $0.15$ dB gain over SCLF and up to $0.2$ dB gain at FER $=10^{-4}$ with optimized CRC allocations. The approach also reduces average decoding time by up to $ ext{29-45}\%$ at higher FERs, while maintaining competitive latency relative to SCLF at moderate FERs, and scales favorably with larger blocklengths. Overall, PSCLF offers a practical path to higher performance and lower latency for polar codes in resource-constrained decoding scenarios.

Abstract

The recently proposed Successive-Cancellation List Flip (SCLF) decoding algorithm for polar codes improves the error-correcting performance of state-of-the-art SC List (SCL) decoding. However, it comes at the cost of a higher complexity. In this paper, we propose the Partitioned SCLF decoding algorithm, an algorithm that divides a word in partitions and applies SCLF decoding to each partition separately. Compared to SCLF, PSCLF allows early termination but is more susceptible to cyclic-redundancy check (CRC) collisions. In order to maximize the coding gain, a new partition design tailored to PSCLF is proposed as well as the possibility to support different CRC lengths. Numerical results show that the proposed PSCLF algorithm has an error-correction performance gain of up to 0.15 dB with respect to SCLF. Moreover, the proposed CRC structure permits to mitigate the error-correction loss at low frame-error rate (FER) due to CRC collisions, showing a gain of 0.2 dB at $\text{FER}=10^{-4}$ with respect to the regular CRC structure. The average execution time of PSCLF is shown to be 1.5 times lower than that of SCLF, and matches the latency of SCLF at $\text{FER}=4\cdot10^{-3}$ and lower.

Figures (7)

• Figure 1: Message $\mathbf{m}'\in\mathbb{F}_2^{K+C}$ allocated in $\mathcal{I}$ for a partitioned polar code with $P=4$ partitions. Dark gray corresponds to the message $\mathbf{m}$ and light gray corresponds to the bits.
• Figure 2: $F(k)$ of $(1024,512+32)$ polar code for $L=4$ and $\frac{E_b}{N_0}=\{1,\,1.5,\, 2,\,2.75\}$ dB.
• Figure 3: $F(k)$ of $(1024,512+32)$ polar code for various list sizes $L$ at $\frac{E_b}{N_0}=2$ dB.
• Figure 4: of $(1024,512+32)$ under SCL, SCLF and PSCLF. and various designs of partitions $\mu$.
• Figure 5: of $(1024,512+32)$ with multiple structures.