IEEE International Conference on Digital Signal Processing (DSP)

A merged BP decoding algorithm for polar-LDPC concatenated codes

Jiaai Liu, Shusen Jing, Xiaohu You, Chuan Zhang

Published Aug 1, 2017• 15 citations

Abstract

Recently, both polar codes and low-density parity-check (LDPC) codes have been adopted by 3GPP eMBB scenario. Since both codes exist in one system, it is natural to consider the concatenation scheme of them. In this paper, a merged belief propagation (BP) decoding algorithm for the concatenated codes of polar and LDPC codes is proposed. By jointing factor graphs, this merged algorithm is designed by serially executing the LDPC and polar decoding. According to numerical results, the bit error rate (BER) of this proposed algorithm can achieve a notable improvement for different code rates compared with the conventional separated approach. For (1024, 512) polar code, the performance gain of the proposed scheme is at least 0 5 dB even at a low BER of 1 × 10-2. Finally, further refinements of computational complexity and hardware implementation are also provided in this paper.

DOI: 10.1109/icdsp.2017.8096145

Related papers

Bipartite Belief Propagation Polar Decoding With Bit-Flipping

Zihao Gong, Yifei Shen, Houren Ji +4 more

For the scenarios with high throughput requirements, the belief propagation (BP) decoding is one of the most promising decoding strategies for polar codes. By pruning the redundant variable nodes (VNs) and check nodes (CNs) in the original factor graph, the graph is condensed to a sparse bipartite graph which is similar to the graph for low-density parity-check (LDPC) codes. In this paper, we introduce the bit-flipping scheme into the LDPC-like BP (L-BP) decoding and propose two methods to identify the error-prone VNs. By additional decoding attempts, the L-BP flip (L-BPF) decoding improves the error-rate performance with a similar average complexity for high Eb=N0values. The simulation results show that the L-BPF decoding achieves 0:25 dB gain compared with the L-BP decoding.

IEEE International Conference on Acoustics Speech and Signal ProcessingApr 9, 20204 citations

An Improved Belief Propagation Decoding of Concatenated Polar Codes With Bit Mapping

Qingping Yu, Zhiping Shi, Li Juan DENG +1 more

Bit-channels of finite-length polar codes are not fully polarized, and the negative influences from semi-polarized channels are not negligible. In this letter, we consider the concatenated system of an inner polar code and an outer low-density parity-check (LDPC) code to improve the error correction performance of finite-length polar code with belief propagation (BP) decoding. We propose a bit mapping method between LDPC coded bits and polarized channels, aiming to match the coding protection of LDPC codes with polarization of polar codes. Simulation results show that, the concatenated polar codes with bit mapping outperform the pure polar codes with BP decoding and concatenated polar codes with traditional consecutive bit mapping.

IEEE Communications LettersApr 20, 201814 citations

Sparse Graphs for Belief Propagation Decoding of Polar Codes

Sebastian Cammerer, Moustafa Ebada, Ahmed Elkelesh +1 more

We describe a novel approach to interpret a polar code as a low-density parity-check (LDPC)-like code with an underlying sparse decoding graph. This sparse graph is based on the encoding factor graph of polar codes and is suitable for conventional belief propagation (BP) decoding. We discuss several pruning techniques based on the check node decoder (CND) and variable node decoder (VND) update equations, significantly reducing the size (i.e., decoding complexity) of the parity-check matrix. As a result, iterative polar decoding can then be conducted on a sparse graph, akin to the traditional well-established LDPC decoding, e.g., using a fully parallel sum-product algorithm (SPA). This facilitates the systematic analysis and design of polar codes using the well-established tools known from analyzing LDPC codes. We show that the proposed iterative polar decoder has a negligible performance loss for short-to-intermediate codelengths compared to Arikan's original BP decoder. Finally, the proposed decoder is shown to benefit from both reduced complexity and reduced memory requirements and, thus, is more suitable for hardware implementations.

arXiv:1712.08538IEEE International Symposium on Information Theory (ISIT)Jun 1, 201858 citations

Improved LDPC-like BPL Decoding Algorithm for Polar Code

Rui Guo, Chenfei Zhang, Chen Lou

To improve the performance of BP decoding for polar codes, researchers have developed a Belief Propagation List (BPL) decoding algorithm by executing multiple BP decoders in parallel.This algorithm outperforms traditional BP decoding based on single graph decoding, although it sacrifices some complexity and delay.Unlike this basic Polar-BPL decoding mentioned above, a low-density parity check like (LDPC-like) BPL decoding algorithm has been introduced into polar codes.This algorithm performs more efficient BP decoding iterations on sparse graphs.To further reduce the complexity and delay of LDPC-like BPL, and avoid analyzing all sparse graphs, this article proposes an improved LDPC-like BPL (ILDPC-like BPL) decoding algorithm based on selecting factor graphs.This algorithm analyzes differences in permuted factor graphs and selects these graphs with non-convergent decoding results to form a decoding list, allowing decoding to be completed with fewer graphs traversed and iterations, thereby reducing complexity and delay.On this basis, to improve the reliability of this algorithm, this article further adds a path metric (PM) mechanism, which can dynamically evaluate different sparse graphs' results in parallel decoding.The simulation results show that compared with LDPC-like BPL (random scheme), ILDPC-like BPL improves decoding performance while reducing decoding delay and complexity; Compared with basic Polar-BPL (cycle-shift scheme), this algorithm greatly reduces decoding delay and complexity while achieving similar performance.

KSII Transactions on Internet and Information SystemsJan 31, 20250 citations

An Improved CRC-Aided BP-BMA Concatenation Decoding for Polar Code

Chenchang Gao, Ming Zhan, Dafa Wen +1 more

Belief propagation (BP) is an iterative and parallel decoding algorithm for polar code that satisfies high throughput and low latency requirements in 5G scenarios. In this work, we proposed a cyclic redundancy check aided belief propagation decoding with the box and match algorithm (CBP-BMA) to enhance the error-correction performance further. This algorithm first runs the BP decoder with early stopping criteria and then uses the soft decoded BP log-likelihood ratio (LLR) as the soft input to the box and match algorithm (BMA) decoder. The simulation results show that even if the reprocessing order of the BMA decoder is as low as one, the proposed algorithm shows a significant improvement than BP decoding. With code rate R=0.5 and code length N=128, the suggested algorithm has a gain of roughly 0.3dB at the desired bit error rate (BER) of 10–3.

International Conference on Communications, Information System and Computer Engineering (CISCE)May 27, 20221 citation

A Transformation for Polar Code BP Decoding

Yi‐Ru Chen, Huang–Chang Lee, Mao‐Chao Lin

A transformation technique has been designed, where the encoding result of the polar code can be transferred to an low-density parity-check (LDPC) code. The belief-propagation decoding can be applied to the received sequence according to the parity-check matrix of the LDPC code. The transferred polar code can provide the same error-rate of the LDPC code, and its performance can be further improved if the success-cancellation decoding is available.

International Symposium on Intelligent Signal Processing and Communication Systems (ISPACS)Dec 1, 20190 citations