The belief propagation (BP) decoding has the advantage of providing soft information iteratively, which allows polar codes to be applicable in scenarios requiring high throughput. However, the unsatisfactory error-correction performance makes the BP polar decoding unable to compete with the successive cancellation list (SCL) decoding that is the baseline algorithm in 3GPP. The BP flip (BPF) decoding offers one option to address this issue through additional decoding attempts with a few bits flipped. However, current BPF decoders yield less efficient flipping accuracy. Considering the complex bit correlation and unanalyzable erroneous bit probability of BPF decoding, we propose a long short-term memory (LSTM) network-assisted BPF (LSTM-BPF) decoding algorithm. Given the soft information output by the original BP decoding, the trained LSTM network achieves more accurate erroneous bit prediction ability. The simulation results show that compared with the state-of-the-art BPF decoders, the LSTM-BPF decoder improves the hit rate of the error bits by 10%, thereby obtaining more than 0.1 dB gains at a frame error rate (FER) of 10-4for polar codes with length 128 and code rate 0.5. The efficient hardware architecture of the proposed LSTM-BPF decoder is designed. By introducing a critical set to reduce the size of the network, the LSTM accelerator could significantly reduce the required computation and storage resources, thereby reducing the inference time.
The belief propagation (BP) decoding has the advantage of providing soft information iteratively, which allows polar codes to be applicable in scenarios requiring high throughput. However, the unsatisfactory error-correction performance makes the BP polar decoding unable to compete with the successive cancellation list (SCL) decoding that is the baseline algorithm in 3GPP. The BP flip (BPF) decoding offers one option to address this issue through additional decoding attempts with a few bits flipped. However, current BPF decoders yield less efficient flipping accuracy. Considering the complex bit correlation and unanalyzable erroneous bit probability of BPF decoding, we propose a long short-term memory (LSTM) network-assisted BPF (LSTM-BPF) decoding algorithm. Given the soft information output by the original BP decoding, the trained LSTM network achieves more accurate erroneous bit prediction ability. The simulation results show that compared with the state-of-the-art BPF decoders, the LSTM-BPF decoder improves the hit rate of the error bits by 10%, thereby obtaining more than 0.1 dB gains at a frame error rate (FER) of 10-4for polar codes with length 128 and code rate 0.5. The efficient hardware architecture of the proposed LSTM-BPF decoder is designed. By introducing a critical set to reduce the size of the network, the LSTM accelerator could significantly reduce the required computation and storage resources, thereby reducing the inference time.
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.
This paper proposes the deep neural network (DNN) based on a belief propagation flip (BPF) decoding algorithm. The conventional BPF decoding does not determine which bits to flip and exhaustively flips the bits of a critical set (CS). This paper uses a DNN to decide which bits to flip. In addition, to reduce the training complexity of DNN, the codeword segmentation and the classes consisting of CS were used. As a result, the proposed BP-DNN-Flip algorithm shows a performance gain of 0.3dB at frame error rate (FER) 10−4compared to the conventional BPF decoding algorithm. In addition, it has a lower average time complexity of at least 55% compared to traditional BPF decoding algorithms at a signal-to-noise ratio (SNR) of 1.5dB.
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.
Known for their capacity-achieving abilities, polar codes have been selected as the control channel coding scheme for 5G communications. To satisfy the needs of high throughput and low latency, belief propagation (BP) is chosen as the decoding algorithm. However, in general, the error performance of BP is worse than that of enhanced successive cancellation (SC). Recently, critical-set bit-flipping (CS-BF) is applied to BP decoding to lower the error rate. However, its trial and error process result in even longer latency. In this work, we propose a convolutional neural network-assisted bit-flipping (CNN-BF) mechanism to further enhance BP decoding of polar codes. With carefully designed input data and model architecture, our proposed CNN-BF can achieve much higher prediction accuracy and better error correction capability than CS-BF but with only half latency. It also achieves a lower block error rate (BLER) than SC list (CA-SCL).
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).