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IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

作者： Kraft, Kira Wehn, Norbert Tech Univ Kaiserslautern Microelect Syst Design Res Grp Kaiserslautern Germany

ISBN: (纸本)9781728176055

Integer Linear Programming (ILP) is a general method to solve the Maximum-Likelihood (ml) decoding problem for all kinds of binary linear codes. To this end, state-of-the-art techniques use a Branch-and-Bound (B&B) framework to partition the underlying integer linear problem into several relaxed linear problems. These linear problems then have to be solved in reasonable time by an efficient Linear Programming (LP) solver. Recently, the Alternating Direction Method of Multipliers (ADMM) has been proposed for efficient software and hardware LP decoding of sparse codes, hence, an ADMM-based ml decoder seems to be a promising approach. In this paper, we investigate this approach with respect to its algorithmic and implementation-specific challenges.

关键词： ml decoding Branch and Bound LP decoding ADMM

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Tight Upper Bounds on the BLER of Spinal Codes Over the AWGN Channel

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IEEE TRANSACTIONS ON COMMUNICATIONS 2025年第1期73卷 332-347页

作者： Li, Aimin Wu, Shaohua Chen, Xiaomeng Sun, Sumei Harbin Inst Technol Shenzhen Guangdong Prov Key Lab Aerosp Commun & Networking Shenzhen 518055 Peoples R China Agcy Sci Technol & Res Inst Infocomm Res Singapore 138632 Singapore Peng Cheng Lab Shenzhen 518055 Peoples R China Harbin Inst Technol Shenzhen Dept Elect Engn Shenzhen 518055 Peoples R China Inst Infocomm Res Agcy Sci Technol & Res ASTAR Fusionopolis Singapore 138632 Singapore

This paper establishes an upper bound on the block error rate (BLER) of Spinal codes, the first rateless codes proven to achieve Shannon capacity in additive white Gaussian noise (AWGN) and binary symmetric channels (BSC). Unlike the conventional reliance on the 1965 Gallager random coding bound for deriving upper bounds, as illustrated in 2016 by Yu et al., this study deviates by noting that Gallager's bound may not adequately represent the distinct properties of specific random codes like Spinal codes and may result in loose bounding performance. We thus introduce novel techniques to refine existing results and enhance the bounding tightness. Our main results are two explicit upper bounds on the BLER of Spinal codes over the AWGN channel, accompanied by theoretical proofs that validate their tightness. Potential applications of the bounds and insights for the coding design are explored in this work.

关键词： Codes Upper bound AWGN channels Error probability Maximum likelihood decoding Spine Hash functions Spinal codes decoding error probability ml decoding upper bounds rateless codes

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Majority Voting With Recursive QAOA and Cost-Restricted Uniform Sampling for Maximum-Likelihood Detection in Massive MIMO

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IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS 2025年第3期24卷 2620-2631页

作者： Gulbahar, Burhan Yasar Univ Dept Elect & Elect Engn TR-35100 Izmir Turkiye

Quantum approximate optimization algorithm (QAOA) with layer depth p is promising near-optimum performance and low complexity for NP-hard maximum-likelihood (ml) detection in nxn multi-input multi-output (MIMO) systems. Experimental challenges for ml detection on Noisy Intermediate-Scale Quantum (NISQ) computers arise from accumulated errors with large p and n. Recursive QAOA (RQAOA) is promising with small p by reducing complexity over n steps. In this article, we modify RQAOA for p << n with cost sorting and post-selection in m << n steps, and then integrate it with majority voting (MV) and successive interference cancellation (SIC) into the QAOA-MVSIC algorithm to tackle experimental challenges. We truncate QAOA circuits to further improve experimental feasibility. Simulations with n=24 and 12 for BPSK and QPSK modulations, respectively, show near-optimum bit-error rate (BER) with p=1 and m <= 4 . Truncated version requires O(mnp) quantum and O(mn2) classical operations with low complexity. We experimentally implement QAOA combined with MV (QAOA-MV) for n is an element of[17,64] in IBM Eagle processor by observing superior performance of QAOA-MV over QAOA and reducing problem dimensions by at least n/4 . We generalize QAOA as cost-restricted uniform sampling (CRUS) oracle and approximately simulate for n <= 128 to obtain comparison benchmark for future QAOA experiments.

关键词： Logic gates Costs Complexity theory Maximum likelihood decoding Circuits Binary phase shift keying Optimization Interference cancellation Integrated circuit modeling Vectors Recursive quantum approximate optimization massive MIMO ml decoding majority voting successive interference cancellation error mitigation

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Low-complexity dominance-based sphere decoder for MIMO systems

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SIGNAL PROCESSING 2013年第9期93卷 2500-2509页

作者： Romano, Gianmarco Ciuonzo, Domenico Rossi, Pierluigi Salvo Palmieri, Francesco Univ Naples 2 Dept Ind & Informat Engn I-81031 Aversa CE Italy

The sphere decoder (SD) is an attractive low-complexity alternative to maximum likelihood (ml) detection in a variety of communication systems. It is also employed in multiple-input multiple-output (MIMO) systems where the computational complexity of the optimum detector grows exponentially with the number of transmit antennas. We propose an enhanced version of the SD based on an additional cost function derived from conditions on worst case interference that we call dominance conditions. The proposed detector, the king sphere decoder (KSD), has a computational complexity that results to be not larger than the complexity of the sphere decoder and numerical simulations show that the complexity reduction is usually quite significant. (c) 2013 Elsevier B.V. All rights reserved.

关键词： Tree-search ml decoding Sphere decoder MIMO

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Two-dimensional half-rate codes using two-dimensional finite-field filter banks

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2007年第12期55卷 5846-5853页

作者： Sartipi, Mina Delgosha, Farshid Fekri, Faramarz Univ Tennessee Dept Comp Sci & Engn Chattanooga TN 37403 USA New York Inst Technol Dept Elect Engn & Comp Sci Old Westbury NY 11568 USA Georgia Inst Technol Sch Elect & Comp Engn Atlanta GA 30332 USA

This correspondence introduces two-dimensional (2-D) filter bank codes (TDFBCs). The synthesis bank of a two-channel two-dimensional filter bank over a finite field is used to design the 2-D) code, and the corresponding analysis bank is used to generate the syndrome of the code. First, we study the encoder of half-rate TDFBCs and show that these linear codes are lattice-cyclic. It is proven that any 2-D) lattice-cyclic code can also be generated by a 2-D) filter bank. Second, we introduce a methodology to design TDFBCs over binary erasure channels. These codes have a simple and efficient maximum-likelihood (ml) decoding algorithm for burst erasures. We show that half-rate TDFBCs of dimensions N-1 X N-2 can recover burst erasures of size up to N-1 X N-2 /2 and N-1/2 X N-2 using the pro posed decoding technique. Finally, we present examples of TDFBCs that satisfy the Reiger bound with equality, i.e., they are capable of correcting any burst of size N-1 N-2 /2.

关键词： burst erasures finite-field filter banks ml decoding Reiger bound two-dimensional codes

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Sub-block recovery scheme for iterative decoding of turbo codes with the sub-block structure

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IEICE TRANSACTIONS ON COMMUNICATIONS 2008年第5期E91B卷 1375-1386页

作者： Bai, Chunlong Mielczarek, Bartosz Fair, Ivan J. Krzymien, Witold A. Univ Alberta Dept Elect & Comp Engn Edmonton AB Canada TRLabs Edmonton AB Canada Feedback Ltd Edmonton AB Canada

Wireless communication systems usually employ a concatenated error control coding scheme consisting of an outer error detection code and an inner error correction code. Traditionally, these two codes are decoded separately. When the sub-block structure is used, each data block (input sequence) at the inner encoder consists of several sub-blocks and each of these sub-blocks is protected with the error detection code. The sub-block structure is used in the Wideband CDMA (WCDMA) system specified by the 3rd Generation Partnership Project (3GPP). In this paper, a sub-block recovery scheme is proposed for this concatenated error control coding scheme to utilize the error detection capability introduced by the outer code in the decoding of the inner code. We demonstrate that, if the inner code is a turbo code with a highly structured interleaver and iterative sub-optimal decoding is used, the sub-block recovery scheme is helpful in correcting a typical error pattern, which helps to improve the block error rate performance. We analyze the decoding performance when sub-block recovery is used together with the maximum likelihood (ml) algorithm as well as the log maximum-a-posteriori probability (Log-MAP) and the soft output Viterbi algorithm (SOVA) and demonstrate gains introduced by the sub-block recovery in the latter two cases using computer simulations.

关键词： turbo codes sub-block structure ml decoding SOVA Log-MAP

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Reduced-Complexity ml Detection and Capacity-Optimized Training for Spatial Modulation Systems

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IEEE TRANSACTIONS ON COMMUNICATIONS 2014年第1期62卷 112-125页

作者： Rajashekar, Rakshith Hari, K. V. S. Hanzo, L. Indian Inst Sci Dept Elect Commun Engn Bangalore 560012 Karnataka India Univ Southampton Sch ECS Southampton SO9 5NH Hants England

Spatial Modulation (SM) is a recently developed low-complexity Multiple-Input Multiple-Output scheme that jointly uses antenna indices and a conventional signal set to convey information. It has been shown that the Maximum-Likelihood (ml) detector of an SM system involves joint detection of the transmit antenna index and of the transmitted symbol, hence, the ml search complexity grows linearly with the number of transmit antennas and the size of the signal set. To circumvent the problem, we show that the ml search complexity of an SM system may be rendered independent of the constellation size, provided that the signal set employed is a square- or a rectangular-QAM. Furthermore, we derive bounds for the capacity of the SM system and derive the optimal power allocation between the data and the training sequences by maximizing the worst-case capacity bound of the SM system operating with imperfect channel state information. We show, with the aid of our simulation results, that the proposed detector is ml-optimal, despite its lowest complexity amongst the existing detectors. Furthermore, we show that employing the proposed optimal power allocation provides a substantial gain in terms of the SM system's capacity as well as signal-to-noise ratio compared to its equal-power-allocation counterpart. Finally, we compare the performance of the SM system to that of the conventional Multiple-Input Multiple-Output (MIMO) system and show that the SM system is capable of outperforming the conventional MIMO system by a significant margin, when both the systems are employing optimal power splitting.

关键词： Spatial modulation ml decoding computational complexity training channel estimation

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GLDPC-Staircase AL-FEC codes: a fundamental study and new results

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EURASIP JOURNAL ON WIRELESS COMMUNICATIONS AND NETWORKING 2016年第1期2016卷 1-28页

作者： Mattoussi, Ferdaouss Roca, Vincent Sayadi, Bessem Inria PRIVAT Res Team Grenoble France Alcatel Lucent Bell Labs Paris France

This paper provides fundamentals in the design and analysis of Generalized Low-Density Parity Check (GLDPC)-Staircase codes over the erasure channel. These codes are constructed by extending an LDPC-Staircase code (base code) using Reed-Solomon (RS) codes (outer codes) in order to benefit from more powerful decoders. The GLDPC-Staircase coding scheme adds, in addition to the LDPC-Staircase repair symbols, extra-repair symbols that can be produced on demand and in large quantities, which provides small rate capabilities. Therefore, these codes are extremely flexible as they can be tuned to behave either like predefined rate LDPC-Staircase codes at one extreme, or like a single RS code at another extreme, or like small rate codes. Concerning the code design, we show that RS codes with "quasi" Hankel matrix-based construction fulfill the desired structure properties, and that a hybrid (IT/RS/ml) decoding is feasible that achieves maximum likelihood (ml) correction capabilities at a lower complexity. Concerning performance analysis, we detail an asymptotic analysis method based on density evolution (DE), extrinsic information transfer (EXIT), and the area theorem. Based on several asymptotic and finite length results, after selecting the optimal internal parameters, we demonstrate that GLDPC-Staircase codes feature excellent erasure recovery capabilities, close to that of ideal codes, both with large and very small objects. From this point of view, they outperform LDPC-Staircase and Raptor codes and achieve correction capabilities close to those of RaptorQ codes. Therefore, all these results make GLDPC-Staircase codes a universal Application-Layer FEC (AL-FEC) solution for many situations that require erasure protection such as media streaming or file multicast transmission.

关键词： AL-FEC codes GLDPC codes LDPC-Staircase codes ml decoding DE and EXIT tools Erasure channels

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Quantum Error Correction Via Noise Guessing decoding

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IEEE ACCESS 2023年 11卷 119446-119461页

作者： Cruz, Diogo Monteiro, Francisco A. Coutinho, Bruno C. Inst Telecomunicacoes P-1049001 Lisbon Portugal Univ Lisbon Inst Super Tecn P-1049001 Lisbon Portugal Inst Univ Lisboa ISCTE P-1649026 Lisbon Portugal

Quantum error correction codes (QECCs) play a central role in both quantum communications and quantum computation. Practical quantum error correction codes, such as stabilizer codes, are generally structured to suit a specific use, and present rigid code lengths and code rates. This paper shows that it is possible to both construct and decode QECCs that can attain the maximum performance of the finite blocklength regime, for any chosen code length when the code rate is sufficiently high. A recently proposed strategy for decoding classical codes called GRAND (guessing random additive noise decoding) opened doors to efficiently decode classical random linear codes (RLCs) performing near the maximum rate of the finite blocklength regime. By using noise statistics, GRAND is a noise-centric efficient universal decoder for classical codes, provided that a simple code membership test exists. These conditions are particularly suitable for quantum systems, and therefore the paper extends these concepts to quantum random linear codes (QRLCs), which were known to be possible to construct but whose decoding was not yet feasible. By combining QRLCs and a newly proposed quantum-GRAND, this work shows that it is possible to decode QECCs that are easy to adapt to changing conditions. The paper starts by assessing the minimum number of gates in the coding circuit needed to reach the QRLCs' asymptotic performance, and subsequently proposes a quantum-GRAND algorithm that makes use of quantum noise statistics, not only to build an adaptive code membership test, but also to efficiently implement syndrome decoding

关键词： GRAND ml decoding quantum error correction codes short codes syndrome decoding

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Reduced complexity sphere decoding using probabilistic threshold based Schnorr-Euchner enumeration

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AEU-INTERNATIONAL JOURNAL OF ELECTRONICS AND COMMUNICATIONS 2016年第4期70卷 449-455页

作者： Karthikeyan, Madurakavi Saraswady, Djagadeesan Pondicherry Engn Coll Dept Elect & Commun Engn Pondicherry 605014 India

The use of multiple antennas at both the transmitter and the receiver is the key technology for future wireless communications since it achieves higher spectral efficiency. Symbol decoding at the receiver for such a system is still a challenge. We propose a new enumeration technique, termed as probabilistic threshold-based Schnorr-Euchner (PSE) enumeration, to reduce the complexity of sphere decoding (SD). The conventional SE-SD algorithm visits all nodes satisfying the sphere constraint in ascending order of their branch metric values. However, this algorithm is computationally expensive in real-time scenarios. Therefore, we use a threshold limit for the branch metric values in the Schnorr-Euchner (SE) enumeration which is based on the noise statistics, to reduce the overall complexity. In each layer of the decoding process, the proposed PSE-SD technique performs a threshold test before visiting the next candidate in an SE ordered list. As a result, unlikely nodes, which do not satisfy the threshold test, are pruned earlier than in the conventional SE-SD algorithm. From the simulation results, we examine the influence of the proposed probabilistic threshold for various MIMO configurations and witness that the PSE-SD technique achieves a significant complexity reduction over existing methods with only a negligible performance loss. (C) 2016 Elsevier GmbH. All rights reserved.

关键词： Sphere decoding SE-enumeration MIMO PSE-enumeration ml decoding Lattice decoding

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