Successive-Cancellation Flip and Perturbation Decoder of Polar Codes

TL;DR

This work addresses enhancing error-correction for CRC-aided polar codes using low-complexity decoders. It introduces two SC-based strategies, DSCFP and PDSCF, that fuse flip (DSCF) and perturbation (SCP) decoding within a single SC engine, controlled by parameters $(F_{max},P_{max},\sigma_p^2)$ and yielding $T_{max}$ trials. Empirical results show gains up to roughly 0.375 dB at $\text{BLER}=10^{-6}$ for $N=1024$, $R=1/2$, with average complexity near SC at high SNR; gains persist across code lengths up to $N=2048$ for CRC-aided polar codes. The methods offer a practical trade-off between decoding performance and hardware complexity, enabling improved reliability for next-generation communication systems.

Abstract

In this paper, two decoding algorithms based on Successive Cancellation (SC) are proposed to improve the error-correction performance of cyclic redundancy check (CRC)-aided polar codes while aiming for a low-complexity implementation. Comparisons with Dynamic SC Flip (DSCF) and SC Perturbation (SCP) are carried out since the proposed DSCF and Perturbation (DSCFP) and Perturbed DSCF (PDSCF) algorithms combine both methods. The analysis includes comparisons with several code lengths $N$ and various number of decoding attempts $T_{max}$. For $N=1024$ and the coding rate $R=\frac{1}{2}$, the DSCFP and the SCP algorithms with $T_{max}=17$ are bested by approximately $0.1$\,dB at block error rate (BLER) of $0.001$. At $\text{BLER}=10^{-6}$ and for $T_{max}=64$, the gain is of $0.375$ dB and $>0.5$ dB with respect to DSCF and SCP, respectively. At high signal-to-noise ratio, the average computational complexity of the proposed algorithms is virtually equivalent to that of SC.

Figures (9)

• Figure 1: Error-correction comparison between the bit-flip (SCF-$F_{\text{max}}$scf_intro and DSCF-$F_{\text{max}}$dyn_scf) algorithms and the elementary perturbation decoders SCP-$P_{\text{max}}$SCP for (a) $(1024,496+16)$ and (b) $(256,112+16)$, $(2048,1008+16)$ codes.
• Figure 2: Number of additional trials when required, $T_{\text{max}}=9$.
• Figure 3: Block diagram of -$(F_{\text{max}},P_{\text{max}})$ decoding algorithm.
• Figure 4: Block diagram of PDSCF-$(F_{\text{max}},P_{\text{max}})$ algorithm.
• Figure 5: Memory requirements of and .