Belief propagation decoding of polar codes on permuted factor graphs

Elkelesh, Ahmed; Ebada, Moustafa; Cammerer, Sebastian; Brink, Stephan ten

doi:10.1109/wcnc.2018.8377158

Cited by 71 publications

(82 citation statements)

References 17 publications

(31 reference statements)

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“…20 for achieving decoding convergence. In [89], the reliability of BP messages was improved by incorporated the knowledge of frozen bits, while a CRC was invoked in [141] together with the overcomplete representation of [63] for achieving decoding convergence. Despite these efforts, the BP algorithm did not outperform the SCL or SCS decoders.…”

Section: E Belief Propagationmentioning

confidence: 99%

Polar Codes and Their Quantum-Domain Counterparts

Babar

Egilmez

Xiang

et al. 2020

IEEE Commun. Surv. Tutorials

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Arikan's polar codes are capable of achieving the Shannon's capacity at a low encoding and decoding complexity, while inherently supporting rate adaptation. By virtue of these attractive features, polar codes have provided fierce competition to both the turbo as well as the Low Density Parity Check (LDPC) codes, making its way into the 5G New Radio (NR). Realizing the significance of polar codes, in this paper we provide a comprehensive survey of polar codes, highlighting the major milestones achieved in the last decade. Furthermore, we also provide tutorial insights into the polar encoder, decoders as well as the code construction methods. We also extend our discussions to quantum polar codes with an emphasis on the underlying quantum-to-classical isomorphism and the syndromebased quantum polar codes.

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Section: E Belief Propagationmentioning

confidence: 99%

Polar Codes and Their Quantum-Domain Counterparts

Babar

Egilmez

Xiang

et al. 2020

IEEE Commun. Surv. Tutorials

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“…A CRC is used for BP decoding to either early terminate the BP process [4], or to help select the correct codeword among a list of candidates [6], [7]. However, these CRC utilizations do not take into account the factor graph realization of CRC, on which the BP decoder can be applied.…”

Section: Preliminaries a Polar Codesmentioning

confidence: 99%

“…In [5], a post-processing algorithm is presented which uses a CRC to detect falseconverged errors. In addition, it is observed in [6], [7] that BP decoding on a list of factor graph permutations of polar codes can benefit from CRC to achieve lower error probabilities than when no CRC is used. However, BP decoding in all of the aforementioned works is only applied on the factor graph of polar codes and the CRC is only used to verify the result of BP at each iteration, without exploiting the inherent factor graph of CRC.…”

Section: Introductionmentioning

confidence: 99%

Neural Belief Propagation Decoding of CRC-Polar Concatenated Codes

Doan

Hashemi

Mambou

et al. 2019

ICC 2019 - 2019 IEEE International Conference on Communications (ICC)

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Polar codes are the first class of error correcting codes that provably achieve the channel capacity at infinite code length. They were selected for use in the fifth generation of cellular mobile communications (5G). In practical scenarios such as 5G, a cyclic redundancy check (CRC) is concatenated with polar codes to improve their finite length performance. This is mostly beneficial for sequential successive-cancellation list decoders. However, for parallel iterative belief propagation (BP) decoders, CRC is only used as an early stopping criterion with incremental error-correction performance improvement. In this paper, we first propose a CRC-polar BP (CPBP) decoder by exchanging the extrinsic information between the factor graph of the polar code and that of the CRC. We then propose a neural CPBP (NCPBP) algorithm which improves the CPBP decoder by introducing trainable normalizing weights on the concatenated factor graph. Our results on a 5G polar code of length 128 show that at the frame error rate of 10 −5 and with a maximum of 30 iterations, the error-correction performance of CPBP and NCPBP are approximately 0.25 dB and 0.5 dB better than that of the conventional CRC-aided BP decoder, respectively, while introducing almost no latency overhead.

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“…Unlike [13], where the code itself was changed via concatenating the polar code with a high rate CRC code, the proposed algorithm in this paper proposes a new decoder based on a list of L parallel independent BP decoders without altering the code itself (i.e., no code concatenation is involved), hence it is referred to as "BPL decoder". Compared to the decoder proposed in [13], BPL allows the parallel execution of all graphs and, thus, possibly both higher throughput and lower latency can be achieved. It is worth mentioning that this decoder resembles the one proposed in [15] where Bose-Chaudhuri-Hocquenghem (BCH) and Golay codes are decoded based on multiple BP decoders over different graph realizations.…”

Section: Introductionmentioning

confidence: 99%

Belief Propagation List Decoding of Polar Codes

et al. 2018

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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 lower decoding latency compared to 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.

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Belief propagation decoding of polar codes on permuted factor graphs

Cited by 71 publications

References 17 publications

Polar Codes and Their Quantum-Domain Counterparts

Polar Codes and Their Quantum-Domain Counterparts

Neural Belief Propagation Decoding of CRC-Polar Concatenated Codes

Belief Propagation List Decoding of Polar Codes

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