Low-Latency Reweighted Belief Propagation Decoding for LDPC Codes

doi:10.1109/LCOMM.2012.080312.121307

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Low-Latency Reweighted Belief Propagation Decoding for LDPC Codes

Journal Article•DOI•

Low-Latency Reweighted Belief Propagation Decoding for LDPC Codes

Jingjing Liu¹, R.C. de Lamare¹•Institutions (1)

University of York¹

06 Aug 2012-IEEE Communications Letters (IEEE)-Vol. 16, Iss: 10, pp 1660-1663

TL;DR: Simulation results show that the VFAP-BP algorithm outperforms the standard BP algorithm, and requires a significantly smaller number of iterations when decoding either general or commercial LDPC codes.

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Abstract: In this paper we propose a novel message passing algorithm which exploits the existence of short cycles to obtain performance gains by reweighting the factor graph. The proposed decoding algorithm is called variable factor appearance probability belief propagation (VFAP-BP) algorithm and is suitable for wireless communications applications with low-latency and short blocks. Simulation results show that the VFAP-BP algorithm outperforms the standard BP algorithm, and requires a significantly smaller number of iterations when decoding either general or commercial LDPC codes.

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Study of Buffer-Aided Distributed Space-Time Coding for Cooperative Wireless Networks

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R.C. de Lamare, Tong Peng

17 Sep 2016-arXiv: Information Theory

TL;DR: This work proposes adaptive buffer-aided distributed space-time coding schemes and algorithms with feedback for wireless networks equipped with buffer- aided relays that obtain performance gains over previously reported techniques.

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Abstract: This work proposes adaptive buffer-aided distributed space-time coding schemes and algorithms with feedback for wireless networks equipped with buffer-aided relays. The proposed schemes employ a maximum likelihood receiver at the destination and adjustable codes subject to a power constraint with an amplify-and-forward cooperative strategy at the relays. Each relay is equipped with a buffer and is capable of storing blocks of received symbols and forwarding the data to the destination if selected. Different antenna configurations and wireless channels, such as static block fading channels, are considered. The effects of using buffer-aided relays to improve the bit error rate (BER) performance are also studied. Adjustable relay selection and optimization algorithms that exploit the extra degrees of freedom of relays equipped with buffers are developed to improve the BER performance. We also analyze the pairwise error probability and diversity of the system when using the proposed schemes and algorithms in a cooperative network. Simulation results show that the proposed schemes and algorithms obtain performance gains over previously reported techniques.

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Additional excerpts

...…[95], [96], [97], [98], [99], [100], [101], [102], [104], [105], [106], [107], [108], [109], [110], [111], [112], [113], [114], [115], [116], [117], [122], [119], [120], [121], [125], [122], [123], [124], [126], [127], [128], [129]. and advanced signal processing techniques [28], [29], [30],…...
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Journal Article•DOI•

Conjugate Gradient Adaptive Learning with Tukey's Biweight M-Estimate

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Lu Lu, Yi Yu, Rodrigo C. de Lamare, Xiaomin Yang

19 Mar 2022-arXiv.org

TL;DR: The proposed Tukey’s biweight M-estimate conjugate gradient algorithm can achieve a faster convergence while retaining a reduced computational complexity as compared to the recursive least-squares (RLS) algorithm.

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Abstract: We propose a novel M-estimate conjugate gradient (CG) algorithm, termed Tukey’s biweight M-estimate CG (TbMCG), for system identiﬁcation in impulsive noise environments. In particular, the TbMCG algorithm can achieve a faster convergence while retaining a reduced computational complexity as compared to the recursive least-squares (RLS) algorithm. Speciﬁcally, the Tukey’s biweight M-estimate incorporates a constraint into the CG ﬁlter to tackle impulsive noise environments. Moreover, the convergence behavior of the TbMCG algorithm is analyzed. Simulation results conﬁrm the excellent performance of the proposed TbMCG algorithm for system identiﬁcation and active noise control applications.

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Posted Content•

Locally-Optimized Reweighted Belief Propagation for Decoding LDPC Codes with Finite-Length.

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Jingjing Li, Rodrigo C. de Lamare, Henk Wymeersch

04 Mar 2014-arXiv: Information Theory

TL;DR: Simulations show that the proposed decoding algorithm significantly outperforms the standard message passing and existing reweighting techniques.

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Abstract: In practice, LDPC codes are decoded using message passing methods. These methods offer good performance but tend to converge slowly and sometimes fail to converge and to decode the desired codewords correctly. Recently, tree-reweighted message passing methods have been modified to improve the convergence speed at little or no additional complexity cost. This paper extends this line of work and proposes a new class of locally optimized reweighting strategies, which are suitable for both regular and irregular LDPC codes. The proposed decoding algorithm first splits the factor graph into subgraphs and subsequently performs a local optimization of reweighting parameters. Simulations show that the proposed decoding algorithm significantly outperforms the standard message passing and existing reweighting techniques.

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Cites background or methods from "Low-Latency Reweighted Belief Propa..."

...The algorithms considered are URW-BP from [6], VFAP-BP from [7], and the proposed LOW-BP algorithm (with T = 1)....
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...ForT = 1, to improve convergence in the offline phase, we initializedρ from URW-BP [6] for regular code and from VFAP-BP [7] for irregular code....
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...These concepts were applied to LDPC decoding in [6], [7] where the FAPs were optimized in an offline procedure, subject to additional constraints: in [6], the FAPs were constrained t o be constant, while in [7], the FAPs were constrained to take on two possible values....
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...For regular code, we observe that URW-BP and VFAP-BP outperform standard BP. LOW-BP is able to provide further improvements....
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...The algorithms considered are URW-BP from [6], VFAP-BP from [7], and the proposed LOW-BP algorithm (withT = 1)....
[...]

Posted Content•

Study of Polarization-Driven Shortening for Polar Codes Designed with the Gaussian Approximation.

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Robert M. Oliveira, Rodrigo C. de Lamare

01 Aug 2018-arXiv: Information Theory

TL;DR: Simulations show that the proposed PD-based shortened polar codes outperform existing shorten polar codes.

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Abstract: This paper presents a polarization-driven (PD) shortening technique for the design of rate-compatible polar codes. The proposed shortening strategy consists of reducing the generator matrix by relating its row index with the channel polarization index. We assume that the shortened bits are known by both the encoder and the decoder and employ successive cancellation (SC) for decoding the shortened codes constructed by the proposed PD technique. A performance analysis is then carried out based on the Spectrum Distance (SD). Simulations show that the proposed PD-based shortened polar codes outperform existing shortened polar codes.

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Cites background from "Low-Latency Reweighted Belief Propa..."

...codes [20], [21], [22] and other decoding algorithms [19], [23], [24], [25], [26], [27], [28], [29] can also be studied....
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Posted Content•

Iterative Detection and Decoding for MIMO Systems with Knowledge-Aided Message Passing Algorithms

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Jingjing Liu, Peng Li, Rodrigo C. de Lamare

23 Apr 2013-arXiv: Information Theory

TL;DR: Simulation results show that when used to perform IDD for multi-antenna systems both proposed BP decoding algorithms can consistently outperform existing BP techniques with a small number of decoding iterations.

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Abstract: In this paper, we consider the problem of iterative detection and decoding (IDD) for multi-antenna systems using low-density parity-check (LDPC) codes. The proposed IDD system consists of a soft-input soft-output parallel interference (PIC) cancellation scheme with linear minimum mean-square error (MMSE) receive filters and two novel belief propagation (BP) decoding algorithms. The proposed BP algorithms exploit the knowledge of short cycles in the graph structure and the reweighting factors derived from the hypergraph's expansion. Simulation results show that when used to perform IDD for multi-antenna systems both proposed BP decoding algorithms can consistently outperform existing BP techniques with a small number of decoding iterations.

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Cites background or methods from "Low-Latency Reweighted Belief Propa..."

...[11] P. Li, R. C. de Lamare and R. Fa, “Multiple Feedback Successiv Interference Cancellation Detection for Multiuser MIMO Systems,” IEEE Transactions on Wireless Communications, vol. 10, no. 8, pp. 2434-2439, August 2011....
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...[8] R.C. de Lamare, R. Sampaio-Neto, “Minimum Mean-SquaredError Iterative Successive Parallel Arbitrated Decision Feedback Detectors for DS-CDMA Systems”,IEEE Transactions on Communications, vol. 56, no. 5, May 2008, pp. 778 - 789....
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...[18] J. Liu, R. C. de Lamare, “Low-Latency Reweighted BeliefPropagation Decoding for LDPC Codes,”IEEE Communications Letters, vol. 16, no. 10, pp. 1660-1663, October 2012....
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...[22] C. T. Healy, R. C. de Lamare, “Decoder-Optimised Progressive Edge Growth Algorithms for the Design of LDPC Codes with Low Error Floors”, vol. 16, no. 6, pp. 889-892, 2012....
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...[12] Peng Li, R. C. de Lamare, “Adaptive Decision-Feedback Detection With Constellation Constraints for MIMO Systems,”IEEE Transactions on Vehicular Technology, vol. 61, no. 2, pp. 853-859, Feb. 2012....
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References

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Book•

Low-Density Parity-Check Codes

[...]

Robert G. Gallager¹•Institutions (1)

Massachusetts Institute of Technology¹

01 Jan 1963

TL;DR: A simple but nonoptimum decoding scheme operating directly from the channel a posteriori probabilities is described and the probability of error using this decoder on a binary symmetric channel is shown to decrease at least exponentially with a root of the block length.

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Abstract: A low-density parity-check code is a code specified by a parity-check matrix with the following properties: each column contains a small fixed number j \geq 3 of l's and each row contains a small fixed number k > j of l's. The typical minimum distance of these codes increases linearly with block length for a fixed rate and fixed j . When used with maximum likelihood decoding on a sufficiently quiet binary-input symmetric channel, the typical probability of decoding error decreases exponentially with block length for a fixed rate and fixed j . A simple but nonoptimum decoding scheme operating directly from the channel a posteriori probabilities is described. Both the equipment complexity and the data-handling capacity in bits per second of this decoder increase approximately linearly with block length. For j > 3 and a sufficiently low rate, the probability of error using this decoder on a binary symmetric channel is shown to decrease at least exponentially with a root of the block length. Some experimental results show that the actual probability of decoding error is much smaller than this theoretical bound.

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11,592 citations

"Low-Latency Reweighted Belief Propa..." refers background in this paper

...I. INTRODUCTION LOW-DENSITY parity-check (LDPC) codes are recog-nized as a class of linear block codes which can achieve near-Shannon capacity with linear-time encoding and parallelizable decoding algorithms....
[...]

Journal Article•DOI•

A recursive approach to low complexity codes

[...]

R.M. Tanner¹•Institutions (1)

University of California, Santa Cruz¹

01 Sep 1981-IEEE Transactions on Information Theory

TL;DR: It is shown that choosing a transmission order for the digits that is appropriate for the graph and the subcodes can give the code excellent burst-error correction abilities.

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Abstract: A method is described for constructing long error-correcting codes from one or more shorter error-correcting codes, referred to as subcodes, and a bipartite graph. A graph is shown which specifies carefully chosen subsets of the digits of the new codes that must be codewords in one of the shorter subcodes. Lower bounds to the rate and the minimum distance of the new code are derived in terms of the parameters of the graph and the subeodes. Both the encoders and decoders proposed are shown to take advantage of the code's explicit decomposition into subcodes to decompose and simplify the associated computational processes. Bounds on the performance of two specific decoding algorithms are established, and the asymptotic growth of the complexity of decoding for two types of codes and decoders is analyzed. The proposed decoders are able to make effective use of probabilistic information supplied by the channel receiver, e.g., reliability information, without greatly increasing the number of computations required. It is shown that choosing a transmission order for the digits that is appropriate for the graph and the subcodes can give the code excellent burst-error correction abilities. The construction principles

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3,246 citations

"Low-Latency Reweighted Belief Propa..." refers background in this paper

...Finally, Section V concludes the paper....
[...]
...The advantages of LDPC codes arise from the sparse (low-density) paritycheck matrices which can be uniquely depicted by graphical representations, referred to as Tanner graphs [3]....
[...]

Journal Article•DOI•

Near Shannon limit performance of low density parity check codes

[...]

David J. C. MacKay¹, Radford M. Neal²•Institutions (2)

University of Cambridge¹, University of Toronto²

29 Aug 1996-Electronics Letters

TL;DR: The authors report the empirical performance of Gallager's low density parity check codes on Gaussian channels, showing that performance substantially better than that of standard convolutional and concatenated codes can be achieved.

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Abstract: The authors report the empirical performance of Gallager's low density parity check codes on Gaussian channels. They show that performance substantially better than that of standard convolutional and concatenated codes can be achieved; indeed the performance is almost as close to the Shannon limit as that of turbo codes.

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3,032 citations

Journal Article•DOI•

A new class of upper bounds on the log partition function

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Martin J. Wainwright¹, Tommi S. Jaakkola², Alan S. Willsky²•Institutions (2)

University of California, Berkeley¹, Massachusetts Institute of Technology²

01 Jul 2005-IEEE Transactions on Information Theory

TL;DR: A new class of upper bounds on the log partition function of a Markov random field (MRF) is introduced, based on concepts from convex duality and information geometry, and the Legendre mapping between exponential and mean parameters is exploited.

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Abstract: We introduce a new class of upper bounds on the log partition function of a Markov random field (MRF). This quantity plays an important role in various contexts, including approximating marginal distributions, parameter estimation, combinatorial enumeration, statistical decision theory, and large-deviations bounds. Our derivation is based on concepts from convex duality and information geometry: in particular, it exploits mixtures of distributions in the exponential domain, and the Legendre mapping between exponential and mean parameters. In the special case of convex combinations of tree-structured distributions, we obtain a family of variational problems, similar to the Bethe variational problem, but distinguished by the following desirable properties: i) they are convex, and have a unique global optimum; and ii) the optimum gives an upper bound on the log partition function. This optimum is defined by stationary conditions very similar to those defining fixed points of the sum-product algorithm, or more generally, any local optimum of the Bethe variational problem. As with sum-product fixed points, the elements of the optimizing argument can be used as approximations to the marginals of the original model. The analysis extends naturally to convex combinations of hypertree-structured distributions, thereby establishing links to Kikuchi approximations and variants.

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498 citations

"Low-Latency Reweighted Belief Propa..." refers background in this paper

...Finally, Section V concludes the paper....
[...]
...Recently, Wymeersch et al. [5], [6] introduced the uniformly reweighted BP (URW-BP) algorithm which exploits BP’s distributed nature and reduces the factor appearance probability (FAP) in [4] to a constant value....
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...Additionally, the BP algorithm is capable of producing the exact inference solutions if the graphical model is acyclic (i.e., a tree), while it does not guarantee to converge if the graph possesses short cycles which significantly deteriorate the overall performance [4]....
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Journal Article•DOI•

Selective avoidance of cycles in irregular LDPC code construction

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Tao Tian¹, C. Jones¹, J.D. Villasenor¹, Richard D. Wesel¹•Institutions (1)

University of California, Los Angeles¹

30 Aug 2004-IEEE Transactions on Communications

TL;DR: A Viterbi-like algorithm is proposed that selectively avoids small cycle clusters that are isolated from the rest of the graph and yields codes with error floors that are orders of magnitude below those of random codes with very small degradation in capacity-approaching capability.

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Abstract: This letter explains the effect of graph connectivity on error-floor performance of low-density parity-check (LDPC) codes under message-passing decoding A new metric, called extrinsic message degree (EMD), measures cycle connectivity in bipartite graphs of LDPC codes Using an easily computed estimate of EMD, we propose a Viterbi-like algorithm that selectively avoids small cycle clusters that are isolated from the rest of the graph This algorithm is different from conventional girth conditioning by emphasizing the connectivity as well as the length of cycles The algorithm yields codes with error floors that are orders of magnitude below those of random codes with very small degradation in capacity-approaching capability

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401 citations

"Low-Latency Reweighted Belief Propa..." refers background in this paper

...Specifically, check nodes having a large number of short cycles are more likely to form clusters of small cycles, which significantly obstruct the convergence of BP algorithm within limited iterations [7]....
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