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Techniques for Improving the Finite Length Performance of Sparse Superposition Codes

IEEE TRANSACTIONS ON COMMUNICATIONS 2018年第3期66卷 905-917页

作者： Greig, Adam Venkataramanan, Ramji Univ Cambridge Dept Engn Cambridge CB2 1PZ England

Sparse superposition codes are a recent class of codes introduced by Barron and Joseph for efficient communication over the AWGN channel. With an appropriate power allocation, these codes have been shown to be asymptotically capacity-achieving with computationally feasible decoding. However, a direct implementation of the capacity-achieving construction does not give good finite length error performance. In this paper, we consider sparse superposition codes with approximate message passing (AMP) decoding, and describe a variety of techniques to improve their finite length performance. These include an iterative algorithm for SPARC power allocation, guidelines for choosing codebook parameters, and estimating a critical decoding parameter online instead of precomputation. We also show how partial outer codes can be used in conjunction with AMP decoding to obtain a steep waterfall in the error performance curves. We compare the error performance of AMP-decoded sparse superposition codes with coded modulation using LDPC codes from the WiMAX standard.

关键词： Sparse regression codes approximate message passing low-complexity decoding finite length performance coded modulation

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Generalized low-density parity-check codes based on Hadamard constraints

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IEEE TRANSACTIONS ON INFORMATION THEORY 2007年第3期53卷 1058-1079页

作者： Yue, Guosen Ping, Li Wang, Xiaodong NEC Labs Amer Inc Princeton NJ 08540 USA City Univ Hong Kong Dept Elect Engn Kowloon Hong Kong Peoples R China Columbia Univ Dept Elect Engn New York NY 10027 USA

In this paper, we consider the design and analysis of generalized low-density parity-check (GLDPC) codes in AWGN channels. The GLDPC codes are specified by a bipartite Tanner graph, as with standard LDPC codes, but with the single parity-check constraints replaced by general coding constraints. In particular, we consider imposing Hadamard code constraints at the check nodes for a low-rate approach, termed LDPC-Hadamard codes. We introduce a low-complexity message-passing based iterative soft-input soft-output (SISO) decoding algorithm, which employs the a posteriori probability (APP) fast Hadamard transform (FHT) for decoding the Hadamard check codes at each decoding iteration. The achievable capacity with the GLDPC codes is then discussed. A modified LDPC-Hadamard code graph is also proposed. We then optimize the LDPC-Hadamard code ensemble using a low-complexity optimization method based on approximating the density evolution by a one-dimensional dynamic system represented by an extrinsic mutual information transfer (EXIT) chart. Simulation results show that the optimized LDPC-Hadamard codes offer better performance in the low-rate region than low-rate turbo-Hadamard codes, but also enjoy a fast convergence rate. A rate-0.003 LDPC-Hadamard code with large block length can achieve a bit-error-rate (BER) performance of 10(-5) at -1.44 dB, which is only 0.15 dB away from the ultimate Shannon limit (-1.592 dB) and 0.24 dB better than the best performing low-rate turbo-Hadamard codes.

关键词： code optimization extrinsic mutual information transfer (EXIT) chart generalized low-density parity-check (GLDPC) codes low-complexity decoding low-density parity-check (LDPC)-Hadamard codes low-rate

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Simplified receiver design for STBC binary continuous phase modulation

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IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS 2008年第2期7卷 452-457页

作者： Man, Liang Punnoose, Ratish Liu, Huaping Oregon State Univ Sch Elect Engn & Comp Sci Corvallis OR 97331 USA Sandia Natl Labs Inst Syst Engn Dept Livermore CA 94551 USA

Existing space-time codes have focused on multiple-antenna systems with linear modulation schemes such as phase-shift keying and quadrature amplitude modulation. Continuous phase modulation (CPM) is an attractive scheme for digital transmission because of its constant envelope which is needed for power efficient transmitters. Recent research has shown that space-time coded CPM can achieve transmit diversity to improve performance while maintaining the compact spectrum of CPM signals. However, these efforts mainly combine space-time coding (STC) with CPM to achieve spatial diversity at the cost of a high decoding complexity. In this paper, we design space-time block codes (STBC) for binary CPM with modulation index h = 1/2 and derive low-complexity receivers for these systems. The proposed scheme has a much lower decoding complexity than STC CPM with the Viterbi decoder and still achieves near-optimum error performances.

关键词： continuous phase modulation wireless communications space-time block codes low-complexity decoding

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Parallel Concatenated Tree Hadamard Codes

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IEEE COMMUNICATIONS LETTERS 2011年第7期15卷 743-745页

作者： Che, Shuling Wang, Xinmei Xidian Univ State Key Lab ISN Xian Peoples R China

In this letter, a new class of low-rate error-correcting codes named parallel concatenated tree Hadamard codes (CTrHC) are designed. Tree Hadamard codes consist of Hadamard segments which are connected by carefully chosen positions from a Hadamard codeword. With the same encoding and decoding complexity as the parallel concatenated zigzag Hadamard codes, CTrHC with short code length can achieve much better error floor performance illustrated by simulation results.

关键词： Hadamard codes low-rate codes error floor parallel concatenation low-complexity decoding

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Concatenated twist Hadamard codes

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IEEE COMMUNICATIONS LETTERS 2007年第12期11卷 992-994页

作者： Che, Shuling Wang, Peng Wang, Xinmei Xidian Univ State Key Lab ISN Xian Peoples R China City Univ Hong Kong Dept Elect Engn Kowloon Hong Kong Peoples R China

In this letter, a new class of low-rate error-correcting codes named twist Hadamard codes (TwHC) are designed based on two single parity check constraints in biorthogonal Hadamard codes. TwHC consists of two branches zigzag Hadamard codes (ZHC) twisted together. Its decoding complexity is very low with the help of fast Hadamard transform. Simulation results show that, compared with concatenated ZHC, parallel concatenated TwHC can significantly improve error floor performance of short codes.

关键词： Hadamard codes low-rate codes error floor parallel concatenation low-complexity decoding

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Optimized Trellis-Based Min-Max Decoder for NB-LDPC Codes

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IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS II-EXPRESS BRIEFS 2020年第1期67卷 57-61页

作者： Tian, Jing Song, Suwen Lin, Jun Wang, Zhongfeng Nanjing Univ Sch Elect Sci & Engn Nanjing 210023 Jiangsu Peoples R China

Non-binary low-density parity-check (NB-LDPC) codes outperform their binary counterparts in many cases. However, an NB-LDPC decoder usually requires excessive hardware resources and memory consumption. The trellis-based min-max decoding algorithm (TMMA), a well-known algorithm proposed in recent years, achieves good tradeoff between decoding performance and hardware complexity. Note that the check node processing unit (CNU) occupies the most hardware consumption. Based on the TMMA, many simplifications for the CNU have been developed with slight performance loss. The current TMMA with L truncations (L-TMMA) is promising for higher hardware efficiency than others. In this brief, based on the L-TMMA, we propose a new CNU design by incorporating algorithmic transformation and architectural optimization to further reduce the hardware complexity and thereby the critical path without any performance degradation. Synthesis results show that the proposed design achieves the lowest hardware consumption and the highest clock frequency with a small latency compared to the state-of-the-arts. Specifically, it saves more than 1/3 hardware resources compared with its original one.

关键词： decoding Hardware complexity theory Computer architecture Iterative decoding Circuits and systems Error correction codes non-binary LDPC codes iterative decoding min-max decoding algorithm low-complexity decoding VLSI

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Decode-and-Forward-Based Differential Modulation for Cooperative Communication System With Unitary and Nonunitary Constellations

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IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY 2012年第1期61卷 152-165页

作者： Bhatnagar, Manav R. Indian Inst Technol Delhi Dept Elect Engn New Delhi 110016 India

In this paper, we derive a maximum-likelihood (ML) decoder of the differential data in a decode-and-forward (DF)-based cooperative communication system utilizing uncoded transmissions. This decoder is applicable to complex-valued unitary and nonunitary constellations suitable for differential modulation. The ML decoder helps to improve the diversity of the DF-based differential cooperative system using an erroneous relaying node. We also derive a piecewise linear (PL) decoder of the differential data transmitted in the DF-based cooperative system. The proposed PL decoder significantly reduces the decoding complexity, as compared with the proposed ML decoder, with no significant degradation in the receiver performance. Existing ML and PL decoders of the differentially modulated uncoded data in the DF-based cooperative communication system are only applicable to binary modulated signals like binary phase shift keying and binary frequency shift keying, whereas the proposed decoders are applicable to complex-valued unitary and nonunitary constellations suitable for differential modulation under uncoded transmissions. We derive a closed-form expression of the uncoded average symbol error rate (SER) of the proposed PL decoder with M phase-shift keying constellation in a cooperative communication system with a single relay and one source-destination pair. An approximate average SER by ignoring higher order noise terms is also derived for this setup. It is analytically shown on the basis of the derived approximate SER that the proposed PL decoder provides full diversity of second order. In addition, we also derive the approximate SER of the differential DF system with multiple relays at asymptotically high signal-to-noise ratio (SNR) of the source-relay links. It is shown by simulations that the proposed PL decoder in the differential DF cooperative system with more than one relay also achieves the maximum possible diversity.

关键词： Cooperative communication decode-and-forward (DF) protocol differential modulation low-complexity decoding maximum-likelihood decoder symbol error rate (SER)

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Concatenated zigzag Hadamard codes

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IEEE TRANSACTIONS ON INFORMATION THEORY 2006年第4期52卷 1711-1723页

作者： Leung, WKR Yue, GS Ping, L Wang, XD Huawei Technol Co Ltd Res Dept PSMT Shenzhen 518129 Peoples R China NEC Labs Amer Inc Princeton NJ 08540 USA City Univ Hong Kong Dept Elect Engn Kowloon Hong Kong Peoples R China Columbia Univ Dept Elect Engn New York NY 10027 USA

In this correspondence, we introduce a new class of low-rate error correction codes called zigzag Hadamard (ZH) codes and their concatenation schemes. Each member of this class of codes is specified by a highly structured zigzag graph with each segment being a Hadamard codeword. The ZH codes enjoy extremely simple encoding and very low-complexity soft-input-soft-output (SISO) decoding based on a posteriori probability (APP) fast Hadamard transform (FHT) technique. We present an asymptotic performance analysis of the proposed concatenated ZH codes using the extrinsic mutual information transfer (EXIT) chart for infinite-length codes. We also provide a union bound analysis of the error performance for finite-length codes. Furthermore, the concatenated ZH codes are shown to be a good class of codes in the low-rate region. Specifically, a rate-0.0107 concatenated code with three ZH components and an inter-leaver size of 65536 can achieve the bit error rate (BER) performance of 10(-5) at -1.15 dB, which is only 0.44 dB away from the ultimate Shannon limit. The proposed concatenated ZH codes offer similar performance as another class of low-rate codes-the turbo-Hadamard codes, and better performance than superorthogonal turbo codes, with much lower encoding and decoding complexities.

关键词： extrinsic mutual information transfer (EXIT) chart Hadamard codes low-complexity decoding low rate parallel concatenation union bound zigzag codes

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Machine Learning-Aided Efficient decoding of Reed-Muller Subcodes

IEEE JOURNAL ON SELECTED AREAS IN INFORMATION THEORY

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IEEE JOURNAL ON SELECTED AREAS IN INFORMATION THEORY 2023年 4卷 260-275页

作者： Jamali, Mohammad Vahid Liu, Xiyang Makkuva, Ashok Vardhan Mahdavifar, Hessam Oh, Sewoong Viswanath, Pramod Univ Michigan Dept Elect Engn & Comp Sci Ann Arbor MI 48109 USA Univ Washington Paul G Allen Sch Comp Sci & Engn Seattle WA 98195 USA Ecole Polytech Fed Lausanne Sch Comp & Commun Sci CH-1015 Lausanne Switzerland Princeton Univ Dept Elect & Comp Engn Princeton NJ 08540 USA

Reed-Muller (RM) codes achieve the capacity of general binary-input memoryless symmetric channels and are conjectured to have a comparable performance to that of random codes in terms of scaling laws. However, such results are established assuming maximum-likelihood decoders for general code parameters. Also, RM codes only admit limited sets of rates. Efficient decoders such as successive cancellation list (SCL) decoder and recently-introduced recursive projection-aggregation (RPA) decoders are available for RM codes at finite lengths. In this paper, we focus on subcodes of RM codes with flexible rates. We first extend the RPA decoding algorithm to RM subcodes. To lower the complexity of our decoding algorithm, referred to as subRPA, we investigate different approaches to prune the projections. Next, we derive the soft-decision based version of our algorithm, called soft-subRPA, that not only improves upon the performance of subRPA but also enables a differentiable decoding algorithm. Building upon the soft-subRPA algorithm, we then provide a framework for training a machine learning (ML) model to search for good sets of projections that minimize the decoding error rate. Training our ML model enables achieving very close to the performance of full-projection decoding with a significantly smaller number of projections. We also show that the choice of the projections in decoding RM subcodes matters significantly, and our ML-aided projection pruning scheme is able to find a good selection, i.e., with negligible performance degradation compared to the full-projection case, given a reasonable number of projections.

关键词： Reed-muller (RM) codes machine learning low-complexity decoding recursive projection-aggregation (RPA) decoding projection pruning

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Modulation Diversity in Fading Channels with Quantized Receiver

Modulation Diversity in Fading Channels with Quantized Recei...

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IEEE International Symposium on Information Theory (ISIT)

作者： Mohammed, Saif Khan Viterbo, Emanuele Hong, Yi Chockalingam, Ananthanarayanan Linkoping Univ Dept Elect Eng ISY Linkoping Sweden Monash Univ Dept ECSE Melbourne Vic 3800 Australia Indian Inst Sci Dept ECE Bangalore 560012 Karnataka India

ISBN: (纸本)9781457705953

In this paper, we address the design of codes which achieve modulation diversity in block fading single-input single-output (SISO) channels with signal quantization at receiver and low-complexity decoding. With an unquantized receiver, coding based on algebraic rotations is known to achieve modulation coding diversity. On the other hand, with a quantized receiver, algebraic rotations may not guarantee diversity. Through analysis, we propose specific rotations which result in the codewords having equidistant component-wise projections. We show that the proposed coding scheme achieves maximum modulation diversity with a low-complexity minimum distance decoder.

关键词： Bit error rate Fading Quadrature amplitude modulation Quantization Receivers SISO channels Signal to noise ratio block fading SISO channels codecs codewords component-wise projections decoding diversity reception fading channels fading channels low-complexity decoding low-complexity minimum distance decoder maximum modulation diversity modulation coding diversity quantized receiver radio receivers signal quantization single-input single-output channels

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