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Low-Complexity soft-output decoding of Polar Codes

IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS 2014年第5期32卷 958-966页

作者： Fayyaz, Ubaid U. Barry, John R. Georgia Inst Technol Sch Elect & Comp Engn Atlanta GA 30332 USA

The state-of-the-art soft-output decoder for polar codes is a message-passing algorithm based on belief propagation, which performs well at the cost of high processing and storage requirements. In this paper, we propose a low-complexity alternative for soft-output decoding of polar codes that offers better performance but with significantly reduced processing and storage requirements. In particular we show that the complexity of the proposed decoder is only 4% of the total complexity of the belief propagation decoder for a rate one-half polar code of dimension 4096 in the dicode channel, while achieving comparable error-rate performance. Furthermore, we show that the proposed decoder requires about 39% of the memory required by the belief propagation decoder for a block length of 32768.

关键词： Polar codes soft-output decoding turbo equalization

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Flexible soft-output decoding of polar codes

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EURASIP JOURNAL ON WIRELESS COMMUNICATIONS AND NETWORKING 2021年第1期2021卷 1-12页

作者： Lee, Sunghoon Park, Jooyoun Kim, Il-Min Heo, Jun Korea Univ Sch Elect Engn 145 Anam Ro Seoul 02841 South Korea Queens Univ Dept Elect & Comp Engn 99 Univ Ave Kingston ON K7L 3N6 Canada

In this research, we study soft-output decoding of polar codes. Two representative soft-output decoding algorithms are belief propagation (BP) and soft cancellation (SCAN). The BP algorithm has low latency but suffers from high computational complexity. On the other hand, the SCAN algorithm, which is proposed for reduced complexity of soft-output decoding, achieves good decoding performance but suffers from long latency. These two algorithms are suitable only for two extreme cases that need very low latency (but with high complexity) or very low complexity (but with high latency). However, many practical systems may need to work for the moderate cases (i.e., not too high latency and not too high complexity) rather than two extremes. To adapt to the various needs of the systems, we propose a very flexible soft-output decoding framework of polar codes. Depending on which system requirement is most crucial, the proposed scheme can adapt to the systems by controlling the level of parallelism. Numerical results demonstrate that the proposed scheme can effectively adapt to various system requirements by changing the level of parallelism.

关键词： Polar codes soft-output decoding Parallelization

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decoding by Sampling - Part II: Derandomization and soft-output decoding

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IEEE TRANSACTIONS ON COMMUNICATIONS 2013年第11期61卷 4630-4639页

作者： Wang, Zheng Liu, Shuiyin Ling, Cong Univ London Imperial Coll Sci Technol & Med Dept Elect & Elect Engn London SW7 2AZ England Monash Univ Dept Elect & Comp Syst Engn Melbourne Vic 3180 Australia

In this paper, a derandomized algorithm for sampling decoding is proposed to achieve near-optimal performance in lattice decoding. By setting a probability threshold to sample candidates, the whole sampling procedure becomes deterministic, which brings considerable performance improvement and complexity reduction over to the randomized sampling. Moreover, the upper bound on the sample size K, which corresponds to near-maximum likelihood (ML) performance, is derived. We also find that the proposed algorithm can be used as an efficient tool to implement soft-output decoding in multiple-input multiple-output (MIMO) systems. An upper bound of the sphere radius R in list sphere decoding (LSD) is derived. Based on it, we demonstrate that the derandomized sampling algorithm is capable of achieving near-maximum a posteriori (MAP) performance. Simulation results show that near-optimum performance can be achieved by a moderate size K in both lattice decoding and soft-output decoding.

关键词： Lattice decoding sampling algorithms lattice reduction soft-output decoding iterative detection and decoding

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Quantizer design for channel codes with soft-output decoding

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IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY 2005年第2期54卷 495-507页

作者： Bakus, J Khandani, AK Maplesoft Waterloo ON N2V 1K8 Canada Univ Waterloo Waterloo ON N2L 3G1 Canada

A new method of combined source-channel coding for the scalar quantization of a discrete memoryless source is presented, which takes advantage of the reliability information produced by a soft-output channel decoder. Numerical results are presented for a memoryless Gaussian source in conjunction with turbo code showing up to 1-dB improvement in the end-to-end distortion with respect to a traditional channel optimized scalar quantizer. The results include a Gaussian source designed using closed-form expression without the need for a training sequence, as well as image pixels using a training sequence. Furthermore, certain issues related to the effect of the channel mismatch and spectral efficiency of the system are studied. It is shown that the increase in distortion due to a channel mismatch can be substantially reduced by using an adaptive receiver.

关键词： quantization soft-output decoding turbo code

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Error rate estimation based on soft output decoding and its application to turbo coding

Error rate estimation based on soft output decoding and its ...

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IEEE Wireless Communications and Networking Conference

作者： Strinati, Emilio Calvanese Simoens, Sebastien Boutros, Joseph CEA LETI Labs Grenoble France Motorola Labs Paris France ENST Paris France

ISBN: (纸本)9781424406586

In this paper, we investigate reliable error rate estimation techniques for MAC layer adaptive mechanisms. In particular, we propose and analyze a novel error rate estimator based on soft output information available as output of receivers with turbo principle. Contrary to previous works on the subject, we relax the assumption of perfect knowledge of Signal-Noise-to-Ratio (SNR) at the receiver, and we analyze the impact of a SNR estimation error on the error rate estimate. We show that, differently to previous techniques, the proposed estimation method is insensitive to such SNR estimation error. Our analytical and simulation results validate the conclusion.

关键词： soft-output decoding channel state estimation

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soft-Out Successive Cancelation decoding and Its List Version for Polar Codes

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IEEE WIRELESS COMMUNICATIONS LETTERS 2025年第3期14卷 651-655页

作者： Gao, Luqin Wu, Xiaofu Yang, Yufan Hu, Junquan Zhang, Suofei Nanjing Univ Posts & Telecommun Natl Engn Res Ctr Commun & Networking Nanjing 210003 Peoples R China Army Engn Univ PLA Coll Commun Engn Nanjing 210000 Peoples R China Nanjing Univ Posts & Telecommun Sch Internet Things Nanjing 210003 Peoples R China

Unlike the standard successive cancelation (SC) decoding of polar codes, soft cancelation (SCAN) decoding could provide soft outputs, which are required in iterative processing for concatenated polar-coded systems. However, its performance is largely limited due to the absence of a list version. This letter first proposes a novel soft-out SC (SoSC) algorithm, where the left-to-right message-passing akin to the SCAN decoding is performed to get soft outputs whenever the partial-sum update is activated during the SC decoding. This SoSC inherits the mechanism of hard-decisions along the path, which allows us to propose its list version, namely, soft-out SC list (SoSCL) decoding. Compared to the existing SCL-based soft decoding algorithms, the proposed SoSCL has a more rigorous mathematical interpretation and could achieve sound gain in iterative processing for various concatenated polar-coded systems.

关键词： decoding Iterative decoding Polar codes Codes Vectors Scheduling Indexes Standards Wireless communication Telecommunications soft-output decoding SCAN decoding SCL decoding

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Twin-stack decoding of recursive systematic convolutional codes

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IEEE TRANSACTIONS ON COMMUNICATIONS 2001年第7期49卷 1158-1167页

作者： Sivasankaran, R McLaughlin, SW Georgia Inst Technol Sch Elect & Comp Engn Atlanta GA 30332 USA

In this paper, we present a method for soft-in/soft-out sequential decoding of recursive systematic convolutional codes, The proposed decoder, the twin stack decoder, is an extension of the well-known ZJ stack decoder, and it uses two stacks. The use of the two stacks lends itself to the generation of soft outputs, and the decoder is easily incorporated into the iterative "turbo" configuration. Under thresholded decoding, it is observed that the decoder is capable of achieving near-maximum a posteriori bit-error rate performance at moderate to high signal-to-noise ratios (SNRs), Also, in the iterative (turbo) configuration, at moderate SNRs (above 2.0 dB), the performance of the proposed decoder is within 1.5 dB of the BCJR algorithm for a 16-state, R = 1/3, recursive code, but this difference narrows progressively at higher SNRs, The complexity of the decoder asymptotically decreases (with SNR) as 1/(number of states), providing a good tradeoff between computational burden and performance. The proposed decoder is also within 1.0 dB of other well-known suboptimal soft-out decoding techniques.

关键词： concatenated coding sequential decoding soft-output decoding

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Expectation Propagation-Based Sampling decoding: Enhancement and Optimization

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2021年 69卷 195-209页

作者： Wang, Zheng Lyu, Shanxiang Xia, Yili Wu, Qihui Nanjing Univ Aeronaut & Astronaut Key Lab Dynam Cognit Syst Electromagnet Spectrum Minist Ind & Informat Technol Nanjing 211106 Peoples R China Southeast Univ Sch Informat Sci & Engn Natl Mobile Commun Res Lab Nanjing 210096 Peoples R China Jinan Univ Coll Cyber Secur Guangzhou 510632 Peoples R China Southeast Univ Sch Informat Sci & Engn Nanjing 210096 Peoples R China Nanjing Univ Aeronaut Astronaut Key Lab Dynam Cognit Syst Electromagnet Spectrum Minist Ind & Informat Technol Nanjing 211106 Peoples R China

In this paper, the paradigm of expectation propagation (EP) algorithm in large-scale MIMO detection is extended by the sampling decoding in an Markov chain Monte Carlo way to boost the approximation of the target posterior distribution. The proposed EP-based sampling decoding scheme not only theoretically addresses the inherent convergence problem of EP, but also is able to achieve the near-optimal decoding performance with the increment of Markov moves. Specifically, the EP-based independent Metropolis-Hastings (MH) is proposed to guarantee the exponential convergence to the target posterior distribution, thus bridging the EP detector and the sampling decoding as a whole. Meanwhile, the output yielded by the EP detector also provides a good initial setup for the sampling decoding, which results in a better convergence performance in the approximation. To further improve the convergence performance and the decoding efficiency, the EP-based Gibbs sampling is given, where the choice of the standard deviation of the discrete Gaussian distribution in the Markov mixing is also studied for a better decoding performance. Moreover, we extend the proposed EP-based Gibbs sampling decoding to the soft-output decoding in MIMO bit-interleaved coded modulation (BICM) systems, which enjoys a flexible decoding trade-off between performance and complexity by the number of Markov moves.

关键词： Signal processing algorithms Detectors Markov processes Gaussian distribution decoding Standards Convergence EP algorithm sampling decoding MIMO detection soft-output decoding lattice decoding near-ML decoding

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Bit-optimal decoding of codes whose Tanner graphs are trees

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DISCRETE APPLIED MATHEMATICS 2003年第1期128卷 293-303页

作者： Soljanin, E Offer, E Lucent Technol Bell Labs Murray Hill NJ 07974 USA Tech Univ Munich Inst Comm Eng D-80290 Munich Germany

We introduce a group algebra formulation for bit-optimal decoding of binary block codes. We use this new framework to give a simple algebraic proof that Pearl's and Gallager's belief propagation decoding algorithms are bit-optimal when the Tanner graph of the code is a tree. We believe that these derivations of known results give new insights into the issues of decoding on graphs from the algebraic coding theorist's point of view. (C) 2003 Elsevier Science B.V. All rights reserved.

关键词： bit-optimal decoding iterative decoding soft-output decoding codes on graph

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Bit-optimal decoding of codes whose Tanner graphs are trees

Bit-optimal decoding of codes whose Tanner graphs are trees

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International Workshop on Coding and Cryptography (WCC 2001)

作者： Soljanin, E Offer, E Lucent Technol Bell Labs Murray Hill NJ 07974 USA Tech Univ Munich Inst Comm Eng D-80290 Munich Germany

关键词： bit-optimal decoding iterative decoding soft-output decoding codes on graph

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