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Enhanced Quasi-Maximum Likelihood decoding Based on 2D Modified Min-Sum Algorithm for 5G LDPC Codes

IEEE TRANSACTIONS ON COMMUNICATIONS 2020年第11期68卷 6669-6682页

作者： Kang, Peng Xie, Yixuan Yang, Lei Yuan, Jinhong Univ New South Wales Sch Elect Engn & Telecommun Kensington NSW 2052 Australia Singapore Univ Technol & Design Sci & Math Cluster Singapore 487372 Singapore Chinese Acad Sci Technol & Engn Ctr Space Utilizat Beijing 100094 Peoples R China

We propose a two-dimensional modified min-sum algorithm for the LDPC codes in the fifth generation (5G) networks standard to approach the error performance of the sum-product algorithm (SPA). In the proposed decoding algorithm, we adopt a partial self-correction method followed by message amplification to improve the reliability of the variable-to-check (V2C) messages. To further approach the performance of the maximum likelihood decoding for 5G short LDPC codes, we propose an enhanced quasi-maximum likelihood (EQML) decoding method. The proposed decoding method performs multiple rounds of decoding tests once the first decoding attempt fails, where the decoder inputs of the selected unreliable variable nodes are modified in each decoding test. A novel node selection method based on the sign fluctuation of V2C messages is proposed for the EQML decoding method. We also present a partial pruning stopping (PPS) rule to reduce the decoding complexity by deactivating part of the decoding tests once a valid codeword is found. A lower bound on the error performance is also derived by using the semi-analytical method. Simulation results show that the EQML decoding method outperforms the SPA with the same decoding complexity and other QML decoding methods, and it approaches the Polyanskiy-Poor-Verdu bound within 0.4 dB.

关键词： Maximum likelihood decoding 5G mobile communication complexity theory Iterative decoding Reliability LDPC codes iterative decoding short block lengths low code rates decoding complexity node selection reprocessing

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Efficient inter-carrier interference cancellation transmissions for cooperative networks with frequency offsets

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IET COMMUNICATIONS 2016年第18期10卷 2575-2581页

作者： Li, Yun Jiang, Hua Yu, Yao Du, Sidan Nanjing Univ Sch Elect Sci & Engn Nanjing 210023 Jiangsu Peoples R China Nanjing Tech Univ Sch Sci Nanjing 211800 Jiangsu Peoples R China

This study discusses new frequency reversal orthogonal frequency-division multiplexing schemes for cooperative networks in order to minimise the effect of multiple carrier frequency offsets. Theorem 1 proposed and proved in this study tells that zero-forcing (ZF) decoding is equivalent to maximum-likelihood (ML) decoding if the equivalent channel matrix is complex orthogonal. Frequency reversal Alamouti code for two-relay scenario and new space-frequency codes for more relay nodes scenario are designed under the guidance of Theorem 1. The reversal operations of these codes make the equivalent channel matrix between the relays and the destination complex orthogonalised. Thus, ZF decoding achieves the advantages of ML decoding, and simulation results also confirm that. Benefiting from the simplified ZF decoding method in Theorem 1, the decoding complexity becomes really low.

关键词： cooperative communication intercarrier interference radiofrequency interference relay networks (telecommunication) OFDM modulation wireless channels matrix algebra maximum likelihood decoding interference suppression efficient intercarrier interference cancellation transmissions cooperative networks frequency reversal orthogonal frequency-division multiplexing schemes multiple carrier frequency offset effect minimisation zero-forcing decoding ZF decoding maximum-likelihood decoding ML decoding equivalent channel matrix frequency reversal Alamouti code space-frequency codes relay nodes scenario Theorem 1 decoding complexity

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Design of Irregular LDPC Codes with Optimized Performance-complexity Tradeoff

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IEEE TRANSACTIONS ON COMMUNICATIONS 2010年第2期58卷 489-499页

作者： Smith, Benjamin Ardakani, Masoud Yu, Wei Kschischang, Frank R. Univ Toronto Dept Elect & Comp Engn Toronto ON M5S 3G4 Canada Univ Alberta Dept Elect & Comp Engn Edmonton AB T6G 2M7 Canada

The optimal performance-complexity tradeoff for error-correcting codes at rates strictly below the Shannon limit is a central question in coding theory. This paper proposes a numerical approach for the minimization of decoding complexity for long-block-length irregular low-density parity-check (LDPC) codes. The proposed design methodology is applicable to any binary-input memoryless symmetric channel and any iterative message-passing decoding algorithm with a parallel-update schedule. A key feature of the proposed optimization method is a new complexity measure that incorporates both the number of operations required to carry out a single decoding iteration and the number of iterations required for convergence. This paper shows that the proposed complexity measure can be accurately estimated from a density-evolution and extrinsic-information transfer chart analysis of the code. A sufficient condition is presented for convexity of the complexity measure in the variable edge-degree distribution;when it is not satisfied, numerical experiments nevertheless suggest that the local minimum is unique. The results presented herein show that when the decoding complexity is constrained, the complexity-optimized codes significantly outperform threshold-optimized codes at long block lengths, within the ensemble of irregular codes.

关键词： Convex optimization extrinsic-information transfer (EXIT) charts decoding complexity low-density parity-check (LDPC) codes

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On algebraic soft-decision decoding algorithms for BCH codes

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IEEE TRANSACTIONS ON INFORMATION THEORY 2001年第1期47卷 45-58页

作者： Kamiya, N NEC Corp Ltd C&C Media Res Labs Miyamae Ku Kawasaki Kanagawa 2168555 Japan

In this paper, three algebraic soft-decision decoding algorithms are presented for binary Bose-Chaudhuri-Hocquengham (BCH) codes. Two of these algorithms are based on the bounded distance (BD) +1 generalized minimum-distance (GMD) decoding presented by Berlekamp, and the other is based on Chase decoding. A simple algebraic algorithm is first introduced, and it forms a common basis for the decoding algorithms presented here. Next, efficient ED +1 GMD and ED +2 GMD decoding algorithms are presented. It is shown that, for binary BCH codes with odd designed-minimum-distance d and length n, both the ED +1 GMD and the ED +2 GMD decoding algorithms can be performed with complexity O(nd), The error performance of these decoding algorithms is shown to be significantly superior to that of conventional GMD decoding by computer simulation. Finally, an efficient algorithm is presented for Chase decoding of binary BCH codes. Like a one-pass GMD decoding algorithm, this algorithm produces all necessary error-locator polynomials for Chase decoding in one run.

关键词： Bose-Chaudhuri-Hocquenghem (BCH) codes bounded distance plus t GMD decoding Chase decoding decoding complexity generalized minimum-distance (GMD) decoding soft decision decoding

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High-Throughput Multi-Frame decoding of QC-LDPC Codes With Modified Rejection-Based Minimum Finding

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IEEE ACCESS 2022年 10卷 5378-5389页

作者： Hasani, Alireza Lopacinski, Lukasz Panic, Goran Kraemer, Rolf IHP Leibniz Jnstitut Innovat Mikroelekt D-15236 Frankfurt Oder Germany Brandenburg Tech Univ Cottbus Dept Elect & Comp Engn D-03046 Cottbus Germany

The key computation in the min-sum decoding algorithm of a Low-Density Parity-Check (LDPC) is finding the first two minima and also the location of the first minimum among a set of messages passed from Variable Nodes (VNs) to Check Nodes (CNs) in a Tanner graph. In this paper, we propose a modified rejection-based scheme for this task which is able to find the one-hot sequence of the minimum location instead of its index. We show that this modification effectively reduces the complexity of min-sum decoding algorithm. Additionally, we reveal a pipelining potential in such a rejection-based architecture which facilitates the multi-frame decoding of Low-Density Parity-Check (LDPC) codes and therefore results in an improvement in decoding throughput with bearable hardware overhead. Synthesis and floorplanning in an industrial 28 nm CMOS technology show improved results in terms of throughput, power, and chip area.

关键词： decoding Parity check codes Phase change materials Schedules complexity theory Throughput Indexes decoding complexity decoding throughput LDPC code min-sum decoding one-hot sequence

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Efficient Decoder Design for Low-Density Lattice Codes From the Lattice Viewpoint

IEEE OPEN JOURNAL OF THE COMMUNICATIONS SOCIETY

引用

IEEE OPEN JOURNAL OF THE COMMUNICATIONS SOCIETY 2023年 4卷 1839-1854页

作者： Wang, Xuebo Mow, Wai Ho Hong Kong Univ Sci & Technol Dept Elect & Comp Engn Hong Kong Peoples R China

Low-density lattice codes (LDLCs) achieve near-capacity performance on additive white Gaussian noise (AWGN) channels. The M-Gaussian decoder is the state-of-the-art message passing decoder for LDLCs in terms of the error performance. However, this decoder has complexity O(Md-1) with messages represented by Gaussian mixtures, where d is the degree of an LDLC and M is the number of Gaussian functions for approximating each check node message. In this paper, we establish the correspondence between Gaussian functions for approximating a variable node message and points of a certain lattice. Based on this lattice viewpoint, the problem of approximating a variable node message is formulated as a lattice point enumeration (LPE) problem. Then, an LPE decoder with linear complexity O(d) is proposed. Our simulation results validate that the LPE decoder achieves almost the same error performance as the M-Gaussian decoder.

关键词： Low-density lattice codes message passing decoding complexity lattice point enumeration

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Unequal error protection codes derived from SEC-DED codes

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ELECTRONICS LETTERS 2016年第8期52卷 619-U92页

作者： Reviriego, Pedro Liu, Shan Shan Sanchez-Macian, Alfonso Xiao, Liyi Antonio Maestro, Juan Univ Antonio De Nebrija Escuela Politecn Super C Pirineos 55 Madrid Spain Harbin Inst Technol Ctr Microelect Harbin 15001 Peoples R China

Error correction codes are commonly used to protect the data stored in memories from errors. Among the codes used, single error correction double error detection (SEC-DED) codes are probably the most common due to their simplicity. In some applications, the importance of the bits is different, being some of them critical while others can tolerate some errors. This is the case, for example, in some multimedia and signal processing systems. For those applications, unequal error protection (UEP) codes that provide different protection for different bits can be used. In many cases, the bits that require extra protection are only a few. Therefore, it would be convenient to use a traditional code extended to provide additional protection for a few bits. A simple method to derive UEP codes from SEC-DED codes is presented. The proposed UEP codes protect a few bits against double errors and behave as SEC-DED codes for the rest. Encoding and decoding complexity is only slightly larger than that of an SEC-DED code and the implementation is a simple modification of the SEC-DED implementation.

关键词： error correction codes error detection codes unequal error protection codes SEC-DED codes error correction codes single error correction double error detection codes UEP codes decoding complexity encoding complexity signal processing systems multimedia system

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Decreasing the complexity of LDPC iterative decoders

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IEEE COMMUNICATIONS LETTERS 2005年第7期9卷 634-636页

作者： Bosco, G Montorsi, G Benedetto, S Politecn Torino Dipartimento Elettron Turin Italy

In this letter we analyze the performance of a low-density parity-check iterative decoder which makes use of an additional buffer at its input, whose function is to decrease the overall complexity of the decoding circuit. We propose a semi-analytical technique that permits the evaluation of the optimum buffer length for each analyzed code.

关键词： LDPC codes iterative decoder decoding complexity

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High-Rate and Low-complexity Space-Time Block Codes for 2 x 2 MIMO Systems

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IEEE COMMUNICATIONS LETTERS 2016年第6期20卷 1227-1230页

作者： Vakilian, Vida Mehrpouyan, Hani Calif State Univ Dept Elect & Comp Engn & Comp Sci Bakersfield CA 93311 USA Boise State Univ Dept Elect & Comp Engn Boise ID 83725 USA

The main design criteria for space-time block codes (STBCs) are the code rate, diversity order, coding gain, and low decoder complexity. In this letter, we propose a full-rate full-diversity STBC for 2 x 2 multiple-input multiple-output (MIMO) systems with a substantially lower maximum likelihood (ML) detection complexity than that of existing schemes. This makes the implementation of high-performance full-rate codes feasible for practical systems. Our numerical evaluation shows that the proposed code achieves significantly lower decoding complexity while maintaining a similar performance compared to that of existing rate-2 STBCs.

关键词： Multiple-input multiple-output (MIMO) space-time coding decoding complexity

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Space-time trellis codes with transmit antenna selection

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ELECTRONICS LETTERS 2003年第11期39卷 854-855页

作者： Chen, Z Vucetic, B Jinhong, Y Univ Sydney Sch Elect & Informat Engn Sydney NSW 2006 Australia Univ New S Wales Sch Elect Engn & Telecommun Sydney NSW 2052 Australia

A scheme combining transmit antenna selection (TAS) and space-time trellis code (STTC), which is referred to as the TAS/STTC scheme, is considered. In this scheme, two transmit antennas, which maximise the signal-to-noise ratio (SNR) at the receiver, are chosen to transmit the baseline STTCs designed for two transmit antennas. It is shown by simulation that, similar to two other transmit antenna selection schemes investigated previously by the authors, this scheme also achieves a full diversity order as if all the transmit antennas were used. In addition, this scheme has a fixed low decoding complexity no matter how high the diversity order. Unlike the traditional STTC, this scheme does not have the requirement for minimum memory order to achieve a full diversity order.

关键词： .diversity order trellis codes decoding complexity STTCs scheme combining transmit STTC scheme

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