34:. The code construction is based on a multiple recursive concatenation of a short kernel code which transforms the physical channel into virtual outer channels. When the number of recursions becomes large, the virtual channels tend to either have high reliability or low reliability (in other words, they polarize or become sparse), and the data bits are allocated to the most reliable channels. It is the first code with an explicit construction to provably achieve the
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decoding: the embedding (E) NN, the check-node (F) NN, the bit-node (G) NN, and the embedding-to-LLR (H) NN. The weights of these NNs are determined by estimating the mutual information of the synthetic channels. By the end of training, the weights of the NPD are fixed and can then be used for decoding.
160:
The computational complexity of NPDs is determined by the parameterization of the neural networks, unlike successive cancellation (SC) trellis decoders, whose complexity is determined by the channel model and are typically used for finite-state channels (FSCs). The computational complexity of NPDs is
139:
suggested to employ a convolutional pre-transformation before polar coding. These pre-transformed variant of polar codes were dubbed polarization-adjusted convolutional (PAC) codes. It was shown that the pre-transformation can effectively improve the distance properties of polar codes by reducing the
368:
NPDs can be integrated into SC decoding schemes such as SC list decoding and CRC-aided SC decoding. They are also compatible with non-uniform and i.i.d. input distributions by integrating them into the Honda-Yamamoto scheme. This flexibility allows NPDs to be used in various decoding scenarios,
156:
Neural Polar
Decoders (NPDs) are an advancement in channel coding that combine neural networks (NNs) with polar codes, providing unified decoding for channels with or without memory, without requiring an explicit channel model. They use four neural networks to approximate the functions of polar
95:
Polar codes have some limitations when used in industrial applications. Primarily, the original design of the polar codes achieves capacity when block sizes are asymptotically large with a successive cancellation decoder. However, with the block sizes used in industry, the performance of the
68:, which renders them attractive for many applications. Moreover, the encoding and decoding energy complexity of generalized polar codes can reach the fundamental lower bounds for energy consumption of two dimensional circuitry to within an
104:. Polar performance can be improved with successive cancellation list decoding, but its usability in real applications is still questionable due to very poor implementation efficiencies caused by the iterative approach.
140:
number of minimum-weight and in general small-weight codewords, resulting in the improvement of block error rates under near maximum likelihood (ML) decoding algorithm such as Fano decoding and list decoding . At
126:
agreed to adopt polar codes for the eMBB (Enhanced Mobile
Broadband) control channels for the 5G NR (New Radio) interface. At the same meeting, 3GPP agreed to use LDPC for the corresponding data channel.
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141:
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field trial tests using polar codes for channel coding. The improvements have been introduced so that the channel performance has now almost closed the gap to the
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Aharoni, Ziv; Huleihel, Bashar; Pfister, Henry D.; Permuter, Haim H. (2023-09-06). "Data-Driven Neural Polar Codes for
Unknown Channels With and Without Memory".
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250:
230:
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Arikan, Erdal; Najeeb ul Hassan; Lentmaier, Michael; Montorsi, Guido; Sayir, Jossy (2015). "Challenges and some new directions in channel coding".
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Moradi, Mohsen; Mozammel, Amir; Qin, Kangjian; Arikan, Erdal (2020). "Performance and
Complexity of Sequential Decoding of PAC Codes".
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508:
853:
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M. Rowshan, A. Burg and E. Viterbo, "Polarization-Adjusted
Convolutional (PAC) Codes: Sequential Decoding vs List Decoding," in
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868:
390:"Channel Polarization: A Method for Constructing Capacity-Achieving Codes for Symmetric Binary-Input Memoryless Channels"
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863:
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M. Rowshan, M. Qiu, Y. Xie, X. Gu and J. Yuan, "Channel Coding Toward 6G: Technical
Overview and Outlook," in
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M. Rowshan and J. Yuan, "On the
Minimum Weight Codewords of PAC Codes: The Impact of Pre-Transformation," in
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839:
AFF3CT home page: A Fast
Forward Error Correction Toolbox for high speed polar code simulations in software
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channels (B-DMC) with polynomial dependence on the gap to capacity. Polar codes were developed by
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successive cancellation is poor compared to well-defined and implemented coding schemes such as
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improving error correction performance while maintaining manageable computational complexity.
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is the block length. In contrast, the computational complexity of SC trellis decoders is
119:, which sets the bar for the maximum rate for a given bandwidth and a given noise level.
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E. Arıkan, "From sequential decoding to channel polarization and back again", 2019,
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Wang, Runxin; Honda, Junya; Yamamoto, Hirosuke; Liu, Rongke; Hou, Yi (2015).
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Notably, polar codes have modest encoding and decoding complexity
799:"Polar Coding Without Alphabet Extension for Asymmetric Models"
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and CRC-aided list decoding of conventional polar codes.
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713:"Construction of polar codes for channels with memory"
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is the number of hidden units in the neural networks,
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439:"Energy Consumption of Error Control Coding Circuits"
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IEEE Journal on
Selected Areas in Information Theory
717:2015 IEEE Information Theory Workshop - Fall (ITW)
489:"Huawei achieves 27Gbps 5G speeds with Polar Code"
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334:{\displaystyle O(|{\mathcal {S}}|^{3}N\log _{2}N)}
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582:, vol. 70, no. 2, pp. 1434-1447, Feb. 2021, doi:
111:announced that it had achieved 27 Gbit/s in
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531:IEEE Open Journal of the Communications Society
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46:, a professor of electrical engineering at
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797:Honda, Junya; Yamamoto, Hirosuke (2013).
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580:IEEE Transactions on Vehicular Technology
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365:is the state space of the channel model.
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803:IEEE Transactions on Information Theory
754:IEEE Transactions on Information Theory
394:IEEE Transactions on Information Theory
252:is the dimension of the embedding, and
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38:for symmetric binary-input, discrete,
623:"List Decoding of Arıkan's PAC Codes"
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533:, vol. 5, pp. 2585-2685, 2024, doi:
509:"3GPP RAN1 meeting #87 final report"
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748:Tal, Ido; Vardy, Alexander (2015).
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854:Error detection and correction
750:"List Decoding of Polar Codes"
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437:Blake, Christopher G. (2017).
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358:{\displaystyle {\mathcal {S}}}
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205:{\textstyle O(kdN\log _{2}N)}
144:, such codes outperform both
98:low-density parity-check code
16:Type of error correcting code
617:Yao, Hanwen; Fazeli, Arman;
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7:
535:10.1109/OJCOMS.2024.3390000
10:
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869:Capacity-approaching codes
719:. IEEE. pp. 187–191.
567:10.1109/JSAIT.2023.3312678
725:10.1109/ITWF.2015.7360760
864:Capacity-achieving codes
815:10.1109/TIT.2013.2282305
776:10.1109/TIT.2015.2410251
584:10.1109/TVT.2021.3052550
416:10.1109/TIT.2009.2021379
91:Industrial applications
388:Arikan, Erdal (2009).
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32:error-correcting codes
447:University of Toronto
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649:2021Entrp..23..841Y
146:convolutional codes
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142:short blocklengths
122:In November 2016,
48:Bilkent University
21:information theory
809:(12): 7829–7838.
734:978-1-4673-7852-9
658:10.3390/e23070841
265:{\displaystyle N}
245:{\displaystyle d}
225:{\displaystyle k}
107:In October 2016,
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44:Erdal Arikan
29:linear block
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100:(LDPC) and
25:polar codes
848:Categories
697:2309.03148
640:2005.13711
633:(7): 841.
603:2012.04990
550:1908.09594
494:2016-10-10
474:1504.03916
453:2019-10-18
373:References
102:turbo code
40:memoryless
823:0018-9448
784:0018-9448
767:1206.0050
515:31 August
424:0018-9448
407:0807.3917
323:
194:
135:In 2019,
131:PAC codes
677:34209050
621:(2021).
341:, where
212:, where
85:ε > 0
77:polylog
668:8303677
645:Bibcode
627:Entropy
821:
782:
731:
675:
665:
548:arXiv:
511:. 3GPP
422:
137:Arıkan
109:Huawei
27:are a
762:arXiv
692:arXiv
635:arXiv
598:arXiv
469:arXiv
442:(PDF)
402:arXiv
819:ISSN
780:ISSN
729:ISBN
673:PMID
517:2017
420:ISSN
124:3GPP
62:log
811:doi
772:doi
721:doi
663:PMC
653:doi
412:doi
314:log
185:log
19:In
850::
817:.
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380:^
113:5G
87:.
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23:,
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