Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

International Symposium on Intelligent Signal Processing and Communication Systems (ISPACS)

A Transformation for Polar Code BP Decoding

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

Published Dec 1, 2019• 0 citations
Publisher

Abstract

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.

DOI
10.1109/ispacs48206.2019.8986396

Related papers

A merged BP decoding algorithm for polar-LDPC concatenated codes

Jiaai Liu, Shusen Jing, Xiaohu You +1 more

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.

IEEE International Conference on Digital Signal Processing (DSP)•Aug 1, 2017•15 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:1712.08538•IEEE International Symposium on Information Theory (ISIT)•Jun 1, 2018•58 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 Letters•Apr 20, 2018•14 citations

Belief-propagation with information correction: improved near maximum-likelihood decoding of low-density parity-check codes

Nedeljko Varnica, M.P.C. Fossorier

We propose an improved belief-propagation (BP) decoder for low-density parity-check (LDPC) codes based on channel information correction. We show that our algorithm achieves sizeable performance gains (in waterfall and error floor regions) compared to the standard BP decoder. We verify by examples that the proposed decoder almost achieves the maximum-likelihood decoding performance for short LDPC codes

IEEE International Symposium on Information Theory (ISIT)•Dec 23, 2004•18 citations

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 Processing•Apr 9, 2020•4 citations

Modified Belief Propagation Decoding Algorithm for Low-Density Parity Check Code Based on Oscillation

Satoshi Gounai, Tomoaki Otsuki Ohtsuki, T. Kaneko

A low-density parity check (LDPC) code with the belief propagation (BP) or the log-likelihood ratio belief propagation (LLR-BP) can achieve good bit error rate (BER) performance approaching the Shannon limit. When a parity check matrix of the LDPC code has the cycle, the BP and LLR-BP decoding algorithms achieve approximate maximum a posterior probability (MAP) decoding. Although the decoding algorithms are approximate MAP decoding, LDPC codes can achieve very good BER. For the short and middle length LDPC codes, BER and block error rate (BLER) performances are affected by cycle largely. In each iteration, the magnitudes of a posterior LLRs of some bits oscillate owing to cycles. The oscillation is the dominant error factor in the high Eb/Noregion for short and middle length LDPC codes. In this paper, we extend the definition of oscillation to extrinsic LLR (ex-LLR) derived in the bit node process and propose the modified LLR-BP and the modified UMP-BP decoding algorithms. To reduce effects of oscillating ex-LLRs on decoding, for oscillating ex-LLRs, we add the previous ex-LLR to the current ex-LLR. From the computer simulation, we show that for short and middle length LDPC codes, with a simple modification, our proposed decoding algorithms can improve the conventional LLR-BP and UMP-BP decoding algorithms. In particular, we show that the modified UMP-BP decoding algorithm with low complexity can achieve better BER and BLER than the conventional LLR-BP decoding algorithm

IEEE Vehicular Technology Conference•Sep 8, 2006•15 citations
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.
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.
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.
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.
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.
A low-density parity check (LDPC) code with the belief propagation (BP) or the log-likelihood ratio belief propagation (LLR-BP) can achieve good bit error rate (BER) performance approaching the Shannon limit. When a parity check matrix of the LDPC code has the cycle, the BP and LLR-BP decoding algorithms achieve approximate maximum a posterior probability (MAP) decoding. Although the decoding algorithms are approximate MAP decoding, LDPC codes can achieve very good BER. For the short and middle length LDPC codes, BER and block error rate (BLER) performances are affected by cycle largely. In each iteration, the magnitudes of a posterior LLRs of some bits oscillate owing to cycles. The oscillation is the dominant error factor in the high Eb/Noregion for short and middle length LDPC codes. In this paper, we extend the definition of oscillation to extrinsic LLR (ex-LLR) derived in the bit node process and propose the modified LLR-BP and the modified UMP-BP decoding algorithms. To reduce effects of oscillating ex-LLRs on decoding, for oscillating ex-LLRs, we add the previous ex-LLR to the current ex-LLR. From the computer simulation, we show that for short and middle length LDPC codes, with a simple modification, our proposed decoding algorithms can improve the conventional LLR-BP and UMP-BP decoding algorithms. In particular, we show that the modified UMP-BP decoding algorithm with low complexity can achieve better BER and BLER than the conventional LLR-BP decoding algorithm