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33rd IEEE Annual International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC)

作者： Shu, Yaofeng Zhao, Hui Han, Changhao Beijing Univ Posts & Telecommun Wireless Signal Proc & Network Lab Key Lab Universal Wireless Commun Beijing 100876 Peoples R China

ISBN: (数字)9781665480536

ISBN: (纸本)9781665480536

Compared with binary polar codes, non-binary polar codes exhibit better performance, which is suitable for short packet services of Internet of Things. But its decoding complexity is high (O(2Nlog(2)(N)), where N is the length of the symbol sequence). To make it practical, this paper proposes a sparse neural network (SNN) decoder. Firstly, the polar factor graph is transformed into a bipartite graph which contains variable node and check node. Then, we propose a pruning algorithm to prune the bipartite graph so as to get a sparse graph. After that, the sparse graph is expanded to get the structure of the deep neural network. Optimized by the training of deep learning, the proposed SNN decoding scheme has competitive performance to the traditional Belief-Propagation (BP) decoding scheme. Moreover, the SNN decoder achieves a reduction of 51.7% in the number of connections compared with BP decoding scheme and its decoding latency is significantly lower than the traditional BP.

关键词： non-binary polar codes sparse neural network decoder deep learning

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Simplified Successive-Cancellation List Decoding of non-binary polar codes with Rate-1 Node

Simplified Successive-Cancellation List Decoding of Non-Bina...

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IEEE Wireless Communications and Networking Conference (IEEE WCNC)

作者： Feng, Baoping Liu, Rongke Sun, He Beihang Univ Sch Elect & Informat Engn Beijing Peoples R China

ISBN: (纸本)9781728131061

In this paper, one of the constituent codes, Rate-1 node, is used to simplify Successive-Cancellation List (SCL) decoding of non-binary polar codes for reducing the decoding complexity. First, we derive the Logarithmic Likelihood Ratio based (LLR-based) path metric of non-binary polar codes in SCL decoding. Then we propose that the path metric only depends on the LLR value at the top of Rate-1 node tree, which avoids traversing a complete decoding tree in non-binary SCL decoding. Finally, we design a novel reliability metric, which is used to select the unreliable symbols from the LLRs at the top of Rate-1 node tree. By the proposed metric, we select the unreliable symbols to generate the candidate paths, which avoids splitting paths for all symbols of Rate-1 node in the conventional SCL decoding. Simulation results show that the proposed non-binary SCL decoding reduces significantly the computation and time complexity without the performance loss.

关键词： non-binary polar codes SCL decoding reliability metric Rate-1 node decoding complexity

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Improved Construction for Multiplicative Repetition Based non-binary polar codes

Improved Construction for Multiplicative Repetition Based No...

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2024 Information Theory Workshop

作者： Xu, Rongchi Chen, Peiyao Liu, Ling Zhu, Min Bai, Baoming Xidian Univ State Key Lab ISN Xian 710071 Peoples R China Xidian Univ Guangzhou Inst Technol Guangzhou 510555 Peoples R China

ISBN: (纸本)9798350348941;9798350348934

Conventional construction of non-binary polar codes divides the synthesized channels into the frozen channels and information channels. Each information channel carries one symbol i.e. q bits. However, there are many middle channels with insufficient polarization, which can not carry one symbol of q bits but only i bits, 1 <= i < q, i <= Z, at finite block lengths. In this paper, we consider the bit-level construction for multiplicative repetition (MR) based non-binary polar codes and propose bit-level improved construction for channel degradation method and Monte-Carlo method. Simulation results show that the proposed construction can significantly improve the decoding performance compared with the conventional construction scheme.

关键词： non-binary polar codes channel degrading construction algorithms

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A Lightweight Encoder and Decoder for non-binary polar codes

A Lightweight Encoder and Decoder for Non-Binary Polar Codes

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2023 Congress in Computer Science, Computer Engineering, and Applied Computing, CSCE 2023

作者： Cochachin, Franklin Ghaffari, Fakhreddine Cy Cergy Paris Université Ensea Cnrs Etis Umr 8051 Cergy France

ISBN: (纸本)9798350327595

In this paper, we associate the Cyclic Code-Shift Keying (CCSK) modulation to non-binary polar (NB-polar) codes to have good decoding performance at ultra-low signal-to-noise ratios (SNRs). We show that the kernel transformation of order 2 using kernel coefficients equal to 1 reduces the complexity of the encoder and decoder and does not degrade error-correcting performance. We consider the Successive-Cancellation Min-Sum (SC-MS) decoder. To greatly reduce the complexity of the SC- MS decoder, we choose a small number of most meaningful values at the check node processing. Our simulation results show that the optimized SC- MS decoder presents a negligible performance degradation with respect to the SC decoder. © 2023 IEEE.

关键词： Channel polarization Error correction Low-complexity encoder and decoder non-binary polar codes Successive-Cancellation (SC) Min-Sum decoders

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Design of non-binary polar codes with shaping 18

Design of non-binary polar codes with shaping

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18th International Symposium on Problems of Redundancy in Information and Control Systems, REDUNDANCY 2023

作者： Karakchieva, Liudmila Trifonov, Peter Itmo University Russia

ISBN: (纸本)9798350381528

A method for construction of non-binary polar (sub)codes with shaping is proposed. It is based on the Honda-Yamamoto scheme and does not require multilevel (ML) coding framework. polar codes with conventional Reed-Solomon kernel, as well as the generalized Reed-Solomon kernel are considered. Simulation results show that non-binary polar (sub)codes with generalized Reed-Solomon kernel provide better shaping gain and performance compared to ML binary polar (sub)codes under list successive cancellation decoding. © 2023 IEEE.

关键词： Code construction higher-order modulation non-binary polar codes probabilistic shaping

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Construction and Decoding Algorithms for polar codes based on 2 x 2 non-binary Kernels 10

Construction and Decoding Algorithms for Polar Codes based o...

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10th IEEE International Symposium on Turbo codes & Iterative Information Processing (ISTC)

作者： Yuan, Peihong Steiner, Fabian Tech Univ Munich Inst Commun Engn Munich Germany

ISBN: (纸本)9781538670484

polar codes based on 2 x 2 non-binary kernels are discussed in this work. The kernel over GF(q) is selected by maximizing the polarization effect and using Monte-Carlo simulation. Belief propagation (BP) and successive cancellation (SC) based decoding algorithms are extended to non-binary codes. Additionally, a successive cancellation list (SCL) decoding with a pruned tree is proposed. Simulation results show that the proposed decoder performs very close to a conventional SCL decoder with significantly lower complexity.

关键词： non-binary polar codes kernel selection decoding algorithm

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Modular Arithmetic Erasure Channels and Their Multilevel Channel polarization

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IEEE TRANSACTIONS ON INFORMATION THEORY 2020年第7期66卷 3976-4006页

作者： Sakai, Yuta Iwata, Ken-Ichi Fujisaki, Hiroshi Univ Fukui Grad Sch Engn Fukui 9108507 Japan Natl Univ Singapore Dept Elect & Comp Engn Singapore 119077 Singapore Kanazawa Univ Grad Sch Nat Sci & Technol Kanazawa Ishikawa 9201192 Japan

This study proposes modular arithmetic erasure channels (MAECs), a novel class of erasure-like channels with an input alphabet that need not be binary. This class contains the binary erasure channel (BEC) and some other known erasure-like channels as special cases. For MAECs, we provide recursive formulas of Arikan-like polar transform to simulate channel polarization. In other words, we show that the synthetic channels of MAECs are equivalent to other MAECs. This is a generalization of well-known recursive formulas of the polar transform for BECs. Using our recursive formulas, we also show that a recursive application of the polar transform for MAECs results in multilevel channel polarization, which is an asymptotic phenomenon that is characteristic of non-binary polar codes. Specifically, we establish a method to calculate the limiting proportions of the partially noiseless and noisy channels that are generated as a result of multilevel channel polarization for MAECs. In the particular case of MAECs, this calculation method solves an open problem posed by Nasser (2017) in the study of non-binary polar codes.

关键词： Transforms Monte Carlo methods Limiting Electronic mail Memoryless systems Channel models non-binary polar codes multilevel channel polarization partially noiseless channels asymptotic distribution generalized erasure channels

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non-binary polar Coded System for the Two-User Multiple-Access Channel

Non-Binary Polar Coded System for the Two-User Multiple-Acce...

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IEEE International Conference on Communications (ICC)

作者： Liu, Guan-Chen Yu, Qi-Yue Harbin Inst Technol Commun Res Ctr Harbin 150001 Peoples R China

ISBN: (数字)9781538683477

ISBN: (纸本)9781538683477

This paper presents non-binary polar codes for the two-user multiple-access channel (MAC). The bit error rate (BER) performances of the non-binary polar codes with different kernel factors have been investigated in detail to select a proper parameter from GF(q) for the generator matrix. Furthermore, the successive cancellation decoding for the non-binary polar codes in the two-user MAC is introduced in detail. Simulation results show that the choice of the kernel factors has a significant impact on the block error rate (BLER) performance;moreover, the non-binary polar codes provide a better BLER performance than their binary counterpart in the two-user MAC.

关键词： non-binary polar codes two-user multiple-access channel kernel selection successive cancellation (SC) decoding

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