Though BP-based polar decoder has low latency, the BLER performance of it does not outperform the CA-SCL decoder with a large list size, which prevents BP-based decoder from its practical implementation. In this paper, we propose a noise-aided belief propagation list bit-flip (NA-BPLF) decoder by merging BPL with artificial noise and bit flipping. In NA-BPLF, when CA-BPL decoding fails, the error-prone bit is chosen for the bit flipping operations based on the decoding results generated by the previous CA-BPL decoding process, and then artificial noise is superimposed. Simulation results show that NA-BPLF achieves better BLER performance which is close to large list size CA-SCL decoder while still keeping the low latency.
Though BP-based polar decoder has low latency, the BLER performance of it does not outperform the CA-SCL decoder with a large list size, which prevents BP-based decoder from its practical implementation. In this paper, we propose a noise-aided belief propagation list bit-flip (NA-BPLF) decoder by merging BPL with artificial noise and bit flipping. In NA-BPLF, when CA-BPL decoding fails, the error-prone bit is chosen for the bit flipping operations based on the decoding results generated by the previous CA-BPL decoding process, and then artificial noise is superimposed. Simulation results show that NA-BPLF achieves better BLER performance which is close to large list size CA-SCL decoder while still keeping the low latency.
Belief propagation list (BPL) decoding for polar codes has attracted more attention due to its inherent parallel nature. However, a large gap still exists with CRC-aided SCL (CA-SCL) decoding. In this work, an improved segmented belief propagation list decoding based on bit flipping (SBPL-BF) is proposed. On the one hand, the proposed algorithm makes use of the cooperative characteristic in BPL decoding such that the codeword is decoded in different BP decoders. Based on this characteristic, the unreliable bits for flipping could be split into multiple subblocks and could be flipped in different decoders simultaneously. On the other hand, a more flexible and effective processing strategy for the priori information of the unfrozen bits that do not need to be flipped is designed to improve the decoding convergence. In addition, this is the first proposal in BPL decoding which jointly optimizes the bit flipping of the information bits and the code bits. In particular, for bit flipping of the code bits, a H-matrix aided bit-flipping algorithm is designed to enhance the accuracy in identifying erroneous code bits. The simulation results show that the proposed algorithm significantly improves the error-correction performance of BPL decoding for medium and long codes. It is more than 0.25 dB better than the state-of-the-art BPL decoding at a block error rate (BLER) of 10−5, and outperforms CA-SCL decoding in the low signal-to-noise (SNR) region for (1024,0.5) polar codes.
Recently, belief propagation list (BPL) decoding has been proposed to achieve the excellent parallel decoding performance of polar codes with high throughput and low latency. However, the performance gap between BPL decoding and state-of-the-art successive cancellation list (SCL) decoding is still significant at practical SNRs. In this letter, we propose an efficient BPL flip (EBPLF) decoding algorithm for filling this gap. Firstly, an efficient bit-flipping strategy under BPL decoding is proposed to allow multiple bits being flipped more efficiently than the existing bit-flipping strategy. Then, by exploiting the decoding diversity and reliability of each bit over the multiple factor graphs within BPL decoding, an enhanced flip set is constructed to identify the error-prone patterns in an efficient way. Extensive simulation results show that EBPLF decoding outperforms the existing BPLF scheme and approaches the performance of adaptive SCL decoding at practical SNRs with much lower average latency.
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).
Belief propagation (BP) decoding for polar codes has been extensively studied because of its inherent parallelism. However, its performance remains inferior to that of successive cancellation list decoding (SCL) due to the structure of the decoding graph. To improve the block error rate (BLER) performance, the BP correction (BPC) decoding, a post-processing scheme that corrects prior knowledge of the identified code bit, improves convergence by executing additional iterations on the failed BP decoder. Moreover, the BPC decoder demonstrates a better decoding performance than the BP-based bit-flipping decoder. Nevertheless, the additional decoding attempts lead to increased latency. In this article, a modified BPC decoder is proposed to reduce the number of decoding attempts by redefining the correction rules. A new metric is designed to effectively identify the corrected location. Numerical results show that the proposed modified BPC decoder achieves a slight improvement in BLER compared with the original BPC, with a dramatic reduction in average complexity. Furthermore, a higher-order version, named MBPC-Ω, is extended to further improve the performance, where the Ω is the maximum correction order. Numerical results show that the higher-order modified BPC achieves a similar BLER performance to existing multiple bit-flipping BP decoders but has around half the latency overhead. In addition, the proposed MBPC-2 decoder performs better than the cyclic redundancy check-aided SCL (CA-SCL) decoder with list size 4 and is slightly worse than the CA-SCL with list size 8 in high signal-to-noise ratio (SNR) regions but with significant decoding latency reduction.
Noise can help weak information bearing signal to be detected in nonlinear systems by the use of stochastic perturbation. In this letter, we propose a novel belief propagation list (BPL) decoder that relies on artificial noise. The proposed decoder is constructed by using parallel independent BP decoders. Noise with different powers are added to different BP decoders that runs in parallel, and the output of the decoder that pass the early detection and termination criteria check is considered as the recovered data. Adding small amount of noise enables the decoder to handle un-converged errors. The obtained results show that the performance of noise-aided BPL decoder is much better than the performances of BP, successive cancelation (SC), and successive cancelation list (SCL) decoders, and it is a bit behind of cyclic redundancy check aided SCL in terms of bit-error rate performance.
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.