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arXiv:2007.15647

Fast Thresholded SC-Flip Decoding of Polar Codes

Furkan Ercan, Warren J. Gross

Published Jul 30, 2020• 0 citations
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Abstract

SC-Flip (SCF) decoding algorithm shares the attention with the common polar code decoding approaches due to its low-complexity and improved error-correction performance. However, the inefficient criterion for locating the correct bit-flipping position in SCF decoding limits its improvements. Due to its improved bit-flipping criterion, Thresholded SCF (TSCF) decoding algorithm exhibits a superior error-correction performance and lower computational complexity than SCF decoding. However, the parameters of TSCF decoding depend on multiple channel and code parameters, and are obtained via Monte-Carlo simulations. Our main goal is to realize TSCF decoding as a practical polar decoder implementation. To this end, we first realize an approximated threshold value that is independent of the code parameters and precomputations. The proposed approximation has negligible error-correction performance degradation on the TSCF decoding. Then, we validate an alternative approach for forming a critical set that does not require precomputations, which also paves the way to the implementation of the Fast-TSCF decoder. Compared to the existing fast SCF implementations, the proposed Fast-TSCF decoder has $0.24$ to $0.41$ dB performance gain at frame error rate of $10^{-3}$, without any extra cost. Compared to the TSCF decoding, Fast-TSCF does not depend on precomputations and requires $87\%$ fewer decoding steps. Finally, implementation results in TSMC 65nm CMOS technology show that the Fast-TSCF decoder is $20\%$ and $82\%$ more area-efficient than the state-of-the-art fast SCF and fast SC-List decoder architectures, respectively.

DOI
10.48550/arxiv.2007.15647

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SC-Flip (SCF) decoding algorithm shares the attention with the common polar code decoding approaches due to its low-complexity and improved error-correction performance. However, the inefficient criterion for locating the correct bit-flipping position in SCF decoding limits its improvements. Due to its improved bit-flipping criterion, Thresholded SCF (TSCF) decoding algorithm exhibits a superior error-correction performance and lower computational complexity than SCF decoding. However, the parameters of TSCF decoding depend on multiple channel and code parameters, and are obtained via Monte-Carlo simulations. Our main goal is to realize TSCF decoding as a practical polar decoder implementation. To this end, we first realize an approximated threshold value that is independent of the code parameters and precomputations. The proposed approximation has negligible error-correction performance degradation on the TSCF decoding. Then, we validate an alternative approach for forming a critical set that does not require precomputations, which also paves the way to the implementation of the Fast-TSCF decoder. Compared to the existing fast SCF implementations, the proposed Fast-TSCF decoder has 0.240.240.24 to 0.410.410.41 dB performance gain at frame error rate of 10−310^{-3}10−3, without any extra cost. Compared to the TSCF decoding, Fast-TSCF does not depend on precomputations and requires 87%87\%87% fewer decoding steps. Finally, implementation results in TSMC 65nm CMOS technology show that the Fast-TSCF decoder is 20%20\%20% and 82%82\%82% more area-efficient than the state-of-the-art fast SCF and fast SC-List decoder architectures, respectively.
SC-Flip (SCF) decoding algorithm shares the attention with the common polar code decoding approaches due to its low-complexity and improved error-correction performance. However, the inefficient criterion for locating the correct bit-flipping position in SCF decoding limits its improvements. Due to its improved bit-flipping criterion, Thresholded SCF (TSCF) decoding algorithm exhibits a superior error-correction performance and lower computational complexity than SCF decoding. However, the parameters of TSCF decoding depend on multiple channel and code parameters, and are obtained via Monte-Carlo simulations. Our main goal is to realize TSCF decoding as a practical polar decoder implementation. To this end, we first realize an approximated threshold value that is independent of the code parameters and precomputations. The proposed approximation has negligible error-correction performance degradation on the TSCF decoding. Then, we validate an alternative approach for forming a critical set that does not require precomputations, which also paves the way to the implementation of the Fast-TSCF decoder. Compared to the existing fast SCF implementations, the proposed Fast-TSCF decoder has 0.24 to 0.41 dB performance gain at frame error rate of 10-3, without any extra cost. Compared to the TSCF decoding, Fast-TSCF does not depend on precomputations and requires 87% fewer decoding steps. Finally, implementation results in TSMC 65nm CMOS technology show that the Fast-TSCF decoder is 20% and 82% more area-efficient than the state-of-the-art fast SCF and fast SC-List decoder architectures, respectively.
In this paper, we propose the threshold successive cancellation flip (Th-SCF) decoding algorithm for polar codes, which enhances the performance of the SC decoder while maintaining low complexity. Theoretical analysis reveals that Th-SCF asymptotically delays the first error position (FEP, the first part where the SC decoder fails) with probability 1, ensuring high decoding performance. Simulation results show that the Th-SCF algorithm achieves performance comparable to the dynamic SC flip (D-SCF) algorithm, but with a reduction in complexity by eliminating the need for sorting operations. A key contribution of this work is the rigorous theoretical framework supporting the Th-SCF algorithm, distinguishing it from existing SC flip (SCF) decoding methods. This theoretical foundation not only explains the performance improvements but also provides insights into the underlying mechanisms of flipping. The proposed Th-SCF algorithm demonstrates strong performance across a wide range of code lengths and rates, and its performance remains stable within a certain threshold range, indicating its practical applicability in real-world communication systems. These results offer valuable perspectives for the design of efficient flip decoding strategies in 5G and future networks.
Although the SC-Flip decoder can significantly avoids the effects of cumulative errors by flipping the first erroneous bit of the traditional SC decoder, the computational complexity of the SCF increases simultaneously. In this letter, to reduce the computational complexity of the SCF decoder, we investigate the log-likelihood ratio (LLR) values and their distribution related to the erroneous bit-channels, then replace the LLR sorting method of SC-Flip with a new value. By setting a threshold for the bits to flip, we proposed a SC-Flip decoder using effective flip bits (SCF-EF). Simulation results demonstrate that for practical code lengths (1024, 512), SCF-EF can achieve 21.37% complexity reduction at SNR of 0.5dB with negligible loss compared with the BLER performance when correcting all single-errors.
This work presents a fast successive-cancellation list flip (Fast-SCLF) decoding algorithm for polar codes that addresses the high latency issue associated with the successive-cancellation list flip (SCLF) decoding algorithm. We first propose a bit-flipping strategy tailored to the state-of-the-art fast successive-cancellation list (FSCL) decoding that avoids tree-traversal in the binary tree representation of SCLF, thus reducing the latency of the decoding process. We then derive a parameterized path selection error model to accurately estimate the bit index at which the correct decoding path is eliminated from the initial FSCL decoding. The trainable parameter is optimized online based on an efficient supervised learning framework. Simulation results show that for a polar code of length 512 with 256 information bits, with similar error-correction performance and memory consumption, the proposed Fast-SCLF decoder reduces up to 73.4% of the average decoding latency of the SCLF decoder with the same list size at the frame error rate of 10−4, while incurring a maximum computational complexity overhead of 27.6%. For the same polar code of length 512 with 256 information bits and at practical signal-to-noise ratios, the proposed decoder with list size 4 reduces 89.3% and 43.7% of the average complexity and decoding latency of the FSCL decoder with list size 32 (FSCL-32), respectively, while also reducing 83.2% of the memory consumption of FSCL-32. The significant improvements of the proposed decoder come at the cost of 0.07 dB error-correction performance degradation compared with FSCL-32.
There are two main algorithms, successive cancellation (SC) algorithm and brief propagation (BP) algorithm, for decoding polar code. The SC algorithm has better error-correcting performance and the BP algorithm has low latency. The hybrid BP-SC decoding combines these two decoding algorithms and achieves improvements. Furthermore, the successive cancellation flip (SCF) algorithm improves the error-correcting performance for the SC algorithm, but it has higher computation complexity and latency. Based on the hybrid BP-SC decoding, we proposed a hybrid BP-SC/SCF decoding for polar codes in this paper to further improve the error-correcting performance. The result shows our approach outperforms to frame error rates (FER) of the SC decoding and BP decoding at least 0.5-dB and outperforms hybrid BP-SC decoding by 0.2-dB to 0.4-dB. Compared with the SCF decoding, the hybrid BPSC/SCF decoding has a small degradation of FER in a highquality channel but it significantly reduces the average computation complexity.
SC-Flip (SCF) decoding is a low-complexity polar code decoding algorithm alternative to SC-List (SCL) algorithm with small list sizes. To achieve the performance of the SCL algorithm with large list sizes, the Dynamic SC-Flip (DSCF) algorithm was proposed. However, DSCF involves logarithmic and exponential computations that are not suitable for practical hardware implementations. In this work, we propose a simple approximation that replaces the transcendental computations of DSCF decoding. Moreover, we show how to incorporate fast decoding techniques with the DSCF algorithm. With proposed approaches, the computational complexity of DSCF decoding is remarkably reduced while maintaining equivalent decoding performance.