On Finite-Length Performance of Polar Codes: Stopping Sets, Error Floor, and Concatenated Design

Eslami, Ali; Pishro-Nik, Hossein

doi:10.1109/tcomm.2013.012313.110692

Cited by 99 publications

(88 citation statements)

References 37 publications

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“…Eslami et al [8], analyzed stopping trees as well as girth of polar codes and their effects on the performance of BPD. Every information bit in A, has a unique stopping tree rooted at that information bit (the right hand side of the factor graph) with its leaves at the code-bits (the left hand side of the graph).…”

Section: A Leafset Size For Information Bits [8]mentioning

confidence: 99%

“…2(b), is 4. For two information bits with different leafset sizes, under belief propagation decoding, the one with smaller leafset size is more likely to be erased than the information bit with larger leafset [8].…”

Section: A Leafset Size For Information Bits [8]mentioning

confidence: 99%

“…To improve the performance of BPD, several concatenated Polar codes with other block codes have been suggested in literature. Eslami et al [8] proposed to concatenate polar codes and LDPC codes, both of long code lengths (2 15 ), to be used in Optical Transport Network (OTN). This concatenated polar-LDPC code has been shown to outperform LDPC code of the same length at the cost of higher decoding complexity.…”

Section: Introductionmentioning

confidence: 99%

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Concatenated LDPC-polar codes decoding through belief propagation

Abbas

Fan

Chen

et al. 2017

2017 IEEE International Symposium on Circuits and Systems (ISCAS)

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Abstract-Owing to their capacity-achieving performance and low encoding and decoding complexity, polar codes have drawn much research interests recently. Successive cancellation decoding (SCD) and belief propagation decoding (BPD) are two common approaches for decoding polar codes. SCD is sequential in nature while BPD can run in parallel. Thus BPD is more attractive for low latency applications. However BPD has some performance degradation at higher SNR when compared with SCD. Concatenating LDPC with Polar codes is one popular approach to enhance the performance of BPD , where a short LDPC code is used as an outer code and Polar code is used as an inner code. In this work we propose a new way to construct concatenated LDPC-Polar code, which not only outperforms conventional BPD and existing concatenated LDPC-Polar code but also shows a performance improvement of 0.5 dB at higher SNR regime when compared with SCD.

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Section: A Leafset Size For Information Bits [8]mentioning

confidence: 99%

Section: A Leafset Size For Information Bits [8]mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Concatenated LDPC-polar codes decoding through belief propagation

Abbas

Fan

Chen

et al. 2017

2017 IEEE International Symposium on Circuits and Systems (ISCAS)

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“…Although there are some improved SC decoders [2,3], the throughput of these decoders is low and the decoding latency is relatively high. Another interesting decoding method for polar codes is belief propagation (BP) decoding [4][5][6][7][8][9][10][11]. One advantage of BP decoder is its fully parallel architecture which is important for possible applications.…”

Section: Introductionmentioning

confidence: 99%

“…Thus, the proposed BP decoders in [4,5] are based on the factor graph representation of the generator matrix. In this paper, based on the idea of iterative softinput-soft-output decoding of Reed-Solomon (RS) codes [13], we propose an improved BP decoder for polar codes by adapting their parity-check matrices.…”

Section: Introductionmentioning

confidence: 99%

Enhanced belief propagation decoding of polar codes by adapting the parity-check matrix

Jiao

et al. 2017

J Wireless Com Network

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Though the performance of belief propagation (BP) decoder for polar codes is comparable with the successive cancellation (SC) decoder, it has significant performance gap when compared with the improved SC decoders, such as SC list (SCL) decoding. In this paper, we propose an improved BP decoding for polar codes with good performance by adapting their parity-check matrices. The decoding process is iterative and consists of two parts. Firstly, the parity-check matrix of polar codes is adjusted such that one of its submatrices corresponding to less reliable bits is in a sparse nature. Secondly, the BP decoding is applied to the adjusted parity-check matrix. Simulation results show that the proposed decoder, when accompanied with the early termination scheme, provides significant performance gains over the original polar BP decoder under a relatively low decoding complexity and even competes with the cyclic redundancy check (CRC)-aided SCL (CRC-SCL) decoder only by increasing a tolerate complexity.

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Concatenation of polar codes with three‐dimensional parity check (3D‐PC) codes to improve error performance over fading channels

Jasim

Bayat

Uçan

2019

Int J Communication

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SummaryIn this paper, we concatenated of three‐dimensional parity check (3D‐PC) block and polar codes for improving error correction performance and bit error rate (BER). Three different sizes of 3D parity check blocks (4 × 4 × 4, 8 × 8 × 8, and 16 × 16 × 16) are used for polar code concatenation. The 4 × 4 × 4 block returns the best performance, but higher complexity of decoder is needed unlikely. The 8 × 8 × 8 has returned acceptable complexity and good performacne. The complexity of decoder is less in the case of 16 × 16 × 16 with slight performance. The performance of the 3D‐PC is reduced when the codewords length is increased. The experiment considered the presence of additive white Gaussian noise (AWGN) with Rayleigh and Rician fading environments. 3D‐PC and polar code concatenation is more precise with codewords of short length, whereas there is insufficient concatenation accuracy with longer codewords. The outcomes of this study contain comparison between AWGN, Rayleigh, and Rician environments. The AWGN is noticed to have a lesser negative impact on the performance of code. Furthermore, increasing the code length may slightly fill the gap of performance between the concatenated and none concatenated polar codes due to the impact of code length on parity check code performance. Simulation results showed the coding performance in case of the polar code with concatenation and without concatenation for different code lengths. Generally, the 3D‐PC polar code concatenation is drawn the optimal result in AWGN environments.

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On Finite-Length Performance of Polar Codes: Stopping Sets, Error Floor, and Concatenated Design

Cited by 99 publications

References 37 publications

Concatenated LDPC-polar codes decoding through belief propagation

Concatenated LDPC-polar codes decoding through belief propagation

Enhanced belief propagation decoding of polar codes by adapting the parity-check matrix

Concatenation of polar codes with three‐dimensional parity check (3D‐PC) codes to improve error performance over fading channels

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