For polar codes, bit-flipping strategy can significantly improve the error-correction performance of the belief propagation (BP) decoding. However, the existing BP flipping (BPF) decoding algorithms require many attempts, due to their inefficiency in locating the erroneous positions. This leads to high decoding complexity, limiting their practical applications, especially for long polar codes. In this letter, an enhanced BPF (EBPF) decoding algorithm is proposed. It requires fewer flipping attempts, but yields an advanced decoding performance. By better utilizing the reliability and divergence of bit estimations, a novel weighted metric (WM) is introduced to identify the possible erroneous positions. During each new decoding attempt, the EBPF decoding takes turns to flip these positions. Our simulation results show that, with the same number of flipping attempts, the proposed decoding outperforms the generalized BPF (GBPF) decoding and the state-of-the-art BP correction (BPC) decoding.
For polar codes, bit-flipping strategy can significantly improve the error-correction performance of the belief propagation (BP) decoding. However, the existing BP flipping (BPF) decoding algorithms require many attempts, due to their inefficiency in locating the erroneous positions. This leads to high decoding complexity, limiting their practical applications, especially for long polar codes. In this letter, an enhanced BPF (EBPF) decoding algorithm is proposed. It requires fewer flipping attempts, but yields an advanced decoding performance. By better utilizing the reliability and divergence of bit estimations, a novel weighted metric (WM) is introduced to identify the possible erroneous positions. During each new decoding attempt, the EBPF decoding takes turns to flip these positions. Our simulation results show that, with the same number of flipping attempts, the proposed decoding outperforms the generalized BPF (GBPF) decoding and the state-of-the-art BP correction (BPC) decoding.
Since the inherent serial nature of successive cancellation list (SCL) decoding results in a long latency, belief propagation (BP) decoding for polar codes has drawn attention for high-throughput applications. However, its error correction performance is inferior to that of SCL decoding. Therefore, the bit-flipping strategy has been recently applied to BP decoding, which can approach the SCL decoding performance through multiple additional decoding attempts. The original BP flip (BPF) decoding suffers from an inaccurate identification of erroneous bits by a fixed flip set (FS), which has been improved by the generalized BPF (GBPF) decoding. In this article, the GBPF decoding is extended to support multiple bits being flipped in one decoding attempt. In addition, for two types of decoding errors: detected errors and undetected errors, we propose two novel methods to more effectively identify erroneous bits. For detected errors, the concept of loop sets is defined and a loopbased identification method is introduced based on the study of error patterns of BP decoding. On the other hand, a method to generate a more accurate fixed FS is proposed for undetected errors, which considers the bit error distribution under BP decoding. Combining the two methods, the GBPF with merged sets (GBPF-MS) decoding can achieve the SCL-8 performance and outperforms the state-of-the-art BPF, BP list, and SC flip (SCF) decoding, for polar codes with length 1024 and information rate 1/2. Implemented by 40nm CMOS technology, the proposed GBPF-MS decoder with ten flips exhibits an average throughput of 4.19 Gbps at 2.5 dB, which is 1.6× and 1.72× faster than the state-of-the-art SCL-4 and SCF decoders, respectively.
The Belief Propagation (BP) algorithm has the advantages of high-speed decoding and low latency. To improve the block error rate (BLER) performance of the BP-based algorithm, the BP flipping algorithm was proposed. However, the BP flipping algorithm attempts numerous useless flippings for improving the BLER performance. To reduce the number of decoding attempts needed without any loss of BLER performance, in this paper a metric is presented to evaluate the likelihood that the bits would correct the BP flipping decoding. Based on this, a BP-Step-Flipping (BPSF) algorithm is proposed which only traces the unreliable bits in the flip set (FS) to flip and skips over the reliable ones. In addition, a threshold β is applied when the magnitude of the log–likelihood ratio (LLR) is small, and an enhanced BPSF (EBPSF) algorithm is presented to lower the BLER. With the same FS, the proposed algorithm can reduce the average number of iterations efficiently. Numerical results show the average number of iterations for EBPSF-1 decreases by 77.5% when N = 256, compared with the BP bit-flip-1 (BPF-1) algorithm at Eb/N0 = 1.5 dB.
Polar codes is the only coding scheme in the world that has been proved that the Shannon threshold is reachable. Because of the high time delay caused by the serial characteristic of Successive Cancellation (SC) decoding, the Belief Propagation (BP) decoding has received more attention because of its higher throughput. However, because its decoding performance is not as good as SC decoding, Bit-Flip (BF) decoding is used in BP. Aiming at the inaccurate construction of flip set in current bit flipping decoding, this paper proposes a new bit error rate BP BF (BPF) decoding algorithm, which is used to construct flip set. We also propose rough flip set and fine flip set Concept of flip set. The rough flip set is constructed by the variance of the characteristics of data stability. The range of the flip set is reduced by the difference in bit error rate, that is, the fine flip set. The research results show that the algorithm proposed in this paper is superior to the current best decoding algorithms such as BP, Enhanced BPF (EBPF) and Log Likelihood Ratio BPF (BPF-LLR). At the same time, the number of iterations of the algorithm is significantly reduced compared with other bit-flipping decoding algorithms.
Due to the design principle of parallel processing, belief propagation (BP) decoding is attractive, and it provides good error-correction performance compared with successive cancellation (SC) decoding. However, its error-correction performance is still inferior to that of successive cancellation list (SCL) decoding. Consequently, this paper proposes a novel flip-list- (FL)-enabled belief propagation (BP) method to improve the error-correction performance of BP decoding for polar codes with low computational complexity. The proposed technique identifies the vulnerable channel log-likelihood ratio (LLR) that deteriorates the BP decoding result. The FL is utilized to efficiently identify the erroneous channel LLRs and correct them for the next BP decoding attempt. The preprocessed channel LLR through FL improves the error-correction performance with minimal flipping attempts and reduces the computational complexity. The proposed technique was compared with the state-of-the-art BP, i.e., BP bit-flip (BP-BF), generalized BP-flip (GBPF), cyclic redundancy check (CRC)-aided (CA-SCL) decoding, and ordered statistic decoding (OSD), algorithms. Simulation results showed that the FL-BP had an excellent block error rate (BLER) performance gain up to 0.7 dB compared with BP, BP-BF, and GBPF decoder. Besides, the computational complexity was reduced considerably in the high signal-to-noise ratio (SNR) regime compared with the BP-BF and GBPF decoding methods.
Belief propagation (BP) has attracted increasing attention due to its high parallelism. In this letter, a correction method is proposed to improve the block error rate (BLER) performance of the BP decoder for polar codes so that it is comparable to that of the successive cancellation list (SCL) decoder. Compared with BP flipping (BPF) decoding, the proposed decoder focuses on prior knowledge of the code bits in the factor graph. Two strategies have been proposed to construct the correction set. The simulation results show that the BPC decoder exhibits a BLER similar to that of BPF decoder while reducing the average latency and complexity by half. In addition, the BLER of the BPC decoder can approach that of the cyclic redundancy check (CRC)-aided SCL (CA-SCL) decoder in regions with low and medium signal-to-noise ratios (SNRs).
Bit flipping was first used to improve the decoding performance of successive cancellation (SC) decoder. Since SC decoding process is serial, so the first bit that goes wrong in the decoding process will cause several subsequent bits to go wrong, which will suffer from higher decoding delay than belief propagation (BP) parallel decoding. In order to meet the performance of 5G low latency and high reliability, BP decoding algorithm have received a lot of attention. However, at medium and high signal-to-noise ratios (SNR), BP decoding does not perform as well as the SC list (SCL) decoding algorithm. Hence, BP decoding algorithm borrows bit-flip strategies from SC bit flip (SCF) decoder to improve the performance. The performance of BP bit flip (BPF) decoding depends on whether the construction of the flip set is correct, so this letter proposes a flip set construction approach based on the standard deviation of the log-likelihood ratio (LLR) and the reliability weight of polarized channels, which is comparable to the existing BPF decoding, the improved algorithm can identify the error-prone bits more efficiently and improve the decoding performance.