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.
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.
We propose a belief propagation list (BPL) decoder with comparable performance to the successive cancellation list (SCL) decoder of polar codes, which already achieves the maximum likelihood (ML) bound of polar codes for sufficiently large list size L. The proposed decoder is composed of multiple parallel independent belief propagation (BP) decoders based on differently permuted polar code factor graphs. A list of possible transmitted codewords is generated and the one closest to the received vector, in terms of Euclidean distance, is picked. To the best of our knowledge, the proposed BPL decoder provides the best performance of plain polar codes under iterative decoding known so far. The proposed algorithm does not require any changes in the polar code structure itself, rendering the BPL into an alternative to the SCL decoder, equipped with a soft output capability enabling, e.g., iterative detection and decoding to further improve performance. Further benefits are the lower decoding latency than the SCL decoder and the possibility of high throughput implementations. Additionally, we show that a different selection strategy of frozen bit positions can further enhance the error-rate performance of the proposed decoder.
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).
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 (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.
Belief propagation (BP) decoding outputs soft information and can be naturally used in iterative receivers. BP list (BPL) decoding provides comparable error-correction performance to the successive cancellation list (SCL) decoding. In this paper, we firstly introduce an enhanced code construction scheme for BPL decoding to improve its error-correction capability. Then, a GPU-based BPL decoder with adoption of the new code construction is presented. Finally, the proposed BPL decoder is tested on NVIDIA RTX3070 and GTX1060. Experimental results show that the presented BPL decoder with early termination criterion achieves above 1 Gbps throughput on RTX3070 for the code (1024, 512) with 32 lists under good channel conditions.
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.