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Large Kernel Polar Codes with efficient Window Decoding [article]

Fariba Abbasi, Emanuele Viterbo
2020 arXiv   pre-print
In this paper, we modify polar codes constructed with some 2^t x 2^t polarization kernels to reduce the time complexity of the window decoding.  ...  This method is applied to some of the kernels constructed in the literature of size 16 and 32, with different error exponents and scaling exponents such as eNBCH kernel.  ...  An ( = , ) polar code based on the × polarization kernel is a linear block code generated by rows of = ⊗ , and ⊗ is -times Kronecker product of matrix with itself.  ... 
arXiv:2005.11102v2 fatcat:b26efhtlargxtghxaiewk52fzi

Efficient decoding of polar codes with some 16×16 kernels

Grigorii Trofimiuk, Peter Trifonov
2018 2018 IEEE Information Theory Workshop (ITW)  
Simulation results show that polar (sub)codes with 16×16 kernels can outperform polar codes with Arikan kernel, while having lower decoding complexity.  ...  A decoding algorithm for polar codes with binary 16×16 kernels with polarization rate 0.51828 and scaling exponents 3.346 and 3.450 is presented.  ...  CONCLUSIONS In this paper efficient decoding algorithms for some 16 × 16 polarization kernels with polarization rate 0.51828 were proposed.  ... 
doi:10.1109/itw.2018.8613307 dblp:conf/itw/TrofimiukT18 fatcat:zuilf4jyo5hstjmys4awezx33y

Recursive Trellis Processing of Large Polarization Kernels [article]

Peter Trifonov
2021 arXiv   pre-print
A reduced complexity algorithm is presented for computing the log-likelihood ratios arising in the successive cancellation decoder for polar codes with large kernels of arbitrary dimension.  ...  compared to the codes based on Arikan kernel with the same decoding complexity.  ...  An approximate kernel processing method based on box-and-match decoder was suggested in [4] . Some kernels of dimension 16 and 32 were published together with efficient processing algorithms [5] .  ... 
arXiv:2101.08081v2 fatcat:gx4lnh2zszdplewqedhdsj6pea

Polar Subcodes

Peter Trifonov, Vera Miloslavskaya
2016 IEEE Journal on Selected Areas in Communications  
An extension of polar codes is proposed, which allows some of the frozen symbols, called dynamic frozen symbols, to be data-dependent.  ...  The codes with Arikan, extended BCH and Reed-Solomon kernel are considered. The proposed codes are shown to outperform LDPC and turbo codes, as well as polar codes with CRC.  ...  Morozov for help in running simulations for polar codes with Reed-Solomon kernel.  ... 
doi:10.1109/jsac.2015.2504269 fatcat:h54qxgcexzfibdh6wo4s5plmgy

Shortened Polarization Kernels [article]

Grigorii Trofimiuk
2021 arXiv   pre-print
The proposed algorithm is applied to some kernels of sizes 16 and 32 to obtain shortened kernels of sizes from 9 to 31. These kernels are used in mixed-kernel polar codes of various lengths.  ...  Numerical results demonstrate the advantage of polar codes with shortened large kernels compared with shortened and punctured Arikan polar codes, and polar codes with small kernels.  ...  ACKNOWLEDGEMENT This work is partially supported by the Ministry of Science and Higher Education of Russian Federation, passport of goszadanie no. 2019-0898.  ... 
arXiv:2110.07351v1 fatcat:f7a3idifr5e2notf7rxdd2xyjm

On the Successive Cancellation Decoding of Polar Codes with Arbitrary Linear Binary Kernels [article]

Zhiliang Huang, Shiyi Zhang, Feiyan Zhang, Chunjiang Duanmu, Ming Chen
2017 arXiv   pre-print
Simulation results show that 16×16 kernel polar codes offer significant advantages in terms of error performances compared with 2×2 kernel polar codes under SC and list SC decoders.  ...  A method for efficiently successive cancellation (SC) decoding of polar codes with high-dimensional linear binary kernels (HDLBK) is presented and analyzed.  ...  Simulation results show that 16×16 kernel polar codes offer significant advantages in terms of error performances compared with 2 × 2 kernel polar codes under SC and list SC decoders. .  ... 
arXiv:1701.03264v2 fatcat:khryheius5d3perfssmumhnzxm

Hybrid Non-Binary Repeated Polar Codes [article]

Fariba Abbasi, Hessam Mahdavifar, Emanuele Viterbo
2022 arXiv   pre-print
In the proposed scheme, the outer code is a hybrid polar code constructed in two stages, one with a binary kernel and another also with a binary kernel but applied over a binary extension field.  ...  This particular structure inherits low-complexity decoding structures of polar codes while enabling concatenation with an inner non-binary multiplicative repetition scheme.  ...  Ilya Dumer for providing the simulation results of their proposed scheme in [7] .  ... 
arXiv:2106.12122v2 fatcat:tpyhtdlnfnb3zjwpsqzpzsrovq

Binary successive cancellation decoding of polar codes with Reed-Solomon kernel

Peter Trifonov
2014 2014 IEEE International Symposium on Information Theory  
Reduced complexity implementation of the successive cancellation decoding algorithm for polar codes with Reed-Solomon kernel is presented.  ...  The proposed approach is based on the representation of Reed-Solomon codes as Arikan polar codes over F2m with dynamic frozen symbols, and application of list successive cancellation decoding algorithm  ...  EFFICIENT DECODING OF POLAR CODES WITH REED-SOLOMON KERNEL A.  ... 
doi:10.1109/isit.2014.6875379 dblp:conf/isit/Trifonov14 fatcat:p2mqygn5szdghpbkkhn4hqdgte

An advanced architecture with low complexity of partially parallel polar encoder

U. Mahendra Narasimha Raj, E. V. Narayana
2016 2016 International Conference on Communication and Electronics Systems (ICCES)  
As the proposed encoder allows high-throughput encoding with small hardware complexity, it can be systematically applied to the design of any polar code and to any level of parallelism.  ...  In this brief, we analyze the encoding process in the viewpoint of very-large-scale integration implementation and propose a new efficient encoder architecture that is adequate for long polar codes and  ...  For example, a polar code with a length of 16 is implemented with 32 XOR gates and processed with four stages, as depicted in Fig. 1 .  ... 
doi:10.1109/cesys.2016.7889957 fatcat:ogoc7oy2s5b6bi6tjycimthcta

Low-Latency Software Polar Decoders

Pascal Giard, Gabi Sarkis, Camille Leroux, Claude Thibeault, Warren J. Gross
2016 Journal of Signal Processing Systems  
Polar codes are a new class of capacity-achieving error-correcting codes with low encoding and decoding complexity.  ...  Finally, we show that the energy efficiency of the proposed decoders is comparable to state-of-the-art software polar decoders.  ...  Claude Thibeault is a member of ReSMiQ. Warren J. Gross is a member of ReSMiQ and SYTACom.  ... 
doi:10.1007/s11265-016-1157-y fatcat:ozsx2cobevbgtjbiio5qunur3u

Partially Parallel Encoder Architecture for Long Polar Codes

Hoyoung Yoo, In-Cheol Park
2015 IEEE Transactions on Circuits and Systems - II - Express Briefs  
As the proposed encoder allows high-throughput encoding with small hardware complexity, it can be systematically applied to the design of any polar code and to any level of parallelism.  ...  In this brief, we analyze the encoding process in the viewpoint of very-large-scale integration implementation and propose a new efficient encoder architecture that is adequate for long polar codes and  ...  For example, a polar code with a length of 16 is implemented with 32 XOR gates and processed with four stages, as depicted in Fig. 1 .  ... 
doi:10.1109/tcsii.2014.2369131 fatcat:z4fvqojfyfgs7jl42mz6ogfreq

Performance and Complexity of the Sequential Successive Cancellation Decoding Algorithm [article]

Peter Trifonov
2020 arXiv   pre-print
Simulation results illustrating the performance and complexity of the sequential successive cancellation decoding algorithm are presented for the case of polar subcodes with Arikan and large kernels, as  ...  Performance comparison with Arikan PAC and LDPC codes is provided. Furthermore, complete description of the decoding algorithm is presented.  ...  Trofimiuk for providing an implementation of the decoder for polar codes with K 2 kernel, and N. Iakuba for his help with implementation of the sequential decoder.  ... 
arXiv:2012.08139v1 fatcat:l3qif2sqtbh3bglkysbos7yzba

Polar Codes with Mixed-Kernels [article]

Noam Presman, Ofer Shapira, Simon Litsyn
2015 arXiv   pre-print
A generalization of the polar coding scheme called mixed-kernels is introduced. This generalization exploits several homogeneous kernels over alphabets of different sizes.  ...  An asymptotic analysis of the proposed scheme shows that its polarization properties are strongly related to the ones of the constituent kernels.  ...  Nissim Halabi for helpful discussions and for his contribution to the development of the simulation software that produced Section 6 results.  ... 
arXiv:1107.0478v3 fatcat:3uyetxotozbw3cw6ihpxoamo6a

Memory Management in Successive-Cancellation based Decoders for Multi-Kernel Polar Codes [article]

Valerio Bioglio, Carlo Condo, Ingmar Land
2018 arXiv   pre-print
We propose an efficient, generalized memory management framework for implementation of successivecancellation decoding of multi-kernel polar codes.  ...  Multi-kernel polar codes have recently been proposed to construct polar codes of lengths different from powers of two.  ...  MULTI-KERNEL POLAR CODES Multi-kernel polar codes generalize the construction of polar codes by mixing binary kernels of different sizes.  ... 
arXiv:1809.09436v1 fatcat:vojzfoybkfet5aib2ioqzl2vwe

Sequential decoding of polar codes with arbitrary binary kernel

Vera Miloslavskaya, Peter Trifonov
2014 2014 IEEE Information Theory Workshop (ITW 2014)  
The problem of efficient soft-decision decoding of polar codes with any binary kernel is considered.  ...  Numeric results show that the proposed algorithm enables near-ML decoding of polar codes with BCH kernel.  ...  Polar codes An (n = l m , k) polar code based on l × l kernel B is a linear block code generated by k rows of matrix G n = M (n) B ⊗m , where B ⊗m denotes m-times Kronecker product of matrix with itself  ... 
doi:10.1109/itw.2014.6970857 dblp:conf/itw/MiloslavskayaT14 fatcat:u7hvi7hydvhdtopx6b6o5lo3ii
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