Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Globecom

Efficient LDLC Decoder Design from the Lattice Viewpoint

Xuebo Wang, Wai Ho Mow

Published Dec 1, 2019• 3 citations
Publisher

Abstract

Low density lattice codes (LDLCs) have been shown to approach the AWGN channel capacity and can be decoded by a message passing decoder. The messages passed between check nodes and variable nodes are probability density functions, which are approximated by Gaussian mixtures in existing LDLC decoders. However, in the best-known M-Gaussian decoder, the Gaussian mixtures for approximating variable node messages still contain unnecessary Gaussian components, resulting in exponential decoding complexity in the LDLC degree d. In this paper, an efficient LDLC decoder is proposed from the lattice viewpoint, which only finds out important Gaussian components for approximating the variable node messages. The decoding complexity for the proposed decoder is linear in d. Numerical results show that the proposed decoder can achieve significant complexity saving without degrading the performance compared with the M-Gaussian decoder. In particular, the runtime saving is 75.3% when the code length is 10000 and d is 7.

DOI
10.1109/globecom38437.2019.9013874

Related papers

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

Xuebo Wang, Wai Ho Mow

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$O(M^{d-1})$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.

IEEE Open Journal of the Communications Society•Jan 1, 2023•0 citations

Fast Decoding of Low Density Lattice Codes

Shuiyin Liu, Yi Hong, Emanuele Viterbo +2 more

Low density lattice codes (LDLC) are a family of lattice codes that can be decoded efficiently using a message-passing algorithm. In the original LDLC decoder, the message exchanged between variable nodes and check nodes are continuous functions, which must be approximated in practice. A promising method is Gaussian approximation (GA), where the messages are approximated by Gaussian functions. However, current GA-based decoders share two weaknesses: firstly, the convergence of these approximate decoders is unproven; secondly, the best known decoder requires $O(2^d)$ operations at each variable node, where $d$ is the degree of LDLC. It means that existing decoders are very slow for long codes with large $d$. The contribution of this paper is twofold: firstly, we prove that all GA-based LDLC decoders converge sublinearly (or faster) in the high signal-to-noise ratio (SNR) region; secondly, we propose a novel GA-based LDLC decoder which requires only $O(d)$ operations at each variable node. Simulation results confirm that the error correcting performance of proposed decoder is the same as the best known decoder, but with a much lower decoding complexity.

arXiv:1806.05524•Jun 14, 2018•1 citation

The three/two Gaussian parametric LDLC decoder

Ricardo Antonio Parrao Hernandez, Brian M. Kurkoski

Low density lattice codes (LDLC) can be decoded efficiently using iterative decoding, and approach the capacity of the AWGN channel. In the iterative LDLC decoder the messages are Gaussian mixtures. In any implementation, the Gaussian mixtures must be approximated. This work describes a three/two Gaussian parametric LDLC decoder. Internally at the variable node the periodic Gaussian mixtures are approximated with three or two Gaussians, while the messages between nodes are single Gaussians. The proposed approximation is more accurate than the previously-proposed approximation. Numerical results shows that for moderate dimension, e.g. n = 1, 000, the two Gaussian approximation is sufficient for accurate performance. But for large dimension, e.g. n = 10, 000, three Gaussians are needed.

IEEE Information Theory Workshop (ITW)•Oct 1, 2015•3 citations

A Low Density Lattice Decoder via Non-parametric Belief Propagation

Danny Bickson, Alexander Ihler, Harel Avissar +1 more

presented a new family of codes called low density lattice codes (LDLC) that can be decoded efficiently and approach the capacity of the AWGN channel. A linear time iterative decoding scheme which is based on a message-passing formulation on a factor graph is given. In the current work we report our theoretical findings regarding the relation between the LDLC decoder and belief propagation. We show that the LDLC decoder is an instance of non-parametric belief propagation and further connect it to the Gaussian belief propagation algorithm. Our new results enable borrowing knowledge from the non-parametric and Gaussian belief propagation domains into the LDLC domain. Specifically, we give more general convergence conditions for convergence of the LDLC decoder (under the same assumptions of the original LDLC convergence analysis). We discuss how to extend the LDLC decoder from Latin square to full rank, non-square matrices. We propose an efficient construction of sparse generator matrix and its matching decoder. We report preliminary experimental results which show our decoder has comparable symbol to error rate compared to the original LDLC decoder. I.

•Jan 1, 2009•18 citations

A low density lattice decoder via non-parametric belief propagation

Danny Bickson, Alexander Ihler, Harel Avissar +1 more

The recent work of Sommer, Feder and Shalvi presented a new family of codes called low density lattice codes (LDLC) that can be decoded efficiently and approach the capacity of the AWGN channel. A linear time iterative decoding scheme which is based on a message-passing formulation on a factor graph is given. In the current work we report our theoretical findings regarding the relation between the LDLC decoder and belief propagation. We show that the LDLC decoder is an instance of non-parametric belief propagation and further connect it to the Gaussian belief propagation algorithm. Our new results enable borrowing knowledge from the non-parametric and Gaussian belief propagation domains into the LDLC domain. Specifically, we give more general convergence conditions for convergence of the LDLC decoder (under the same assumptions of the original LDLC convergence analysis). We discuss how to extend the LDLC decoder from Latin square to full rank, non-square matrices. We propose an efficient construction of sparse generator matrix and its matching decoder. We report preliminary experimental results which show our decoder has comparable symbol to error rate compared to the original LDLC decoder.

arXiv:0901.3197•Allerton Conference on Communication, Control, and Computing•Sep 1, 2009•5 citations

Hardware Implementation of a Fixed-Point Decoder for Low-Density Lattice Codes

Rachna Srivastava, Vincent Gaudet, Patrick Mitran

Abstract This paper describes a field-programmable gate array (FPGA) implementation of a fixed-point low-density lattice code (LDLC) decoder where the Gaussian mixture messages that are exchanged during the iterative decoding process are approximated to a single Gaussian. A detailed quantization study is first performed to find the minimum number of bits required for the fixed-point decoder to attain a frame error rate (FER) performance similar to floating-point. Then efficient numerical methods are devised to approximate the required non-linear functions. Finally, the paper presents a comparison of the performance of the different decoder architectures as well as a detailed analysis of the resource requirements and throughput trade-offs of the primary design blocks for the different architectures. A novel pipelined LDLC decoder architecture is proposed where resource re-utilization along with pipelining allows for a parallelism equivalent to 50 variable nodes on the target FPGA device. The pipelined architecture attains a throughput of 10.5 Msymbols/sec at a distance of 5 dB from capacity which is a 1.8 $$\times$$ × improvement in throughput compared to an implementation with 20 parallel variable nodes without pipelining. This implementation also achieves 24 $$\times$$ × improvement in throughput over a baseline serial decoder.

Journal of Signal Processing Systems•Jan 1, 2022•1 citation
Low density lattice codes (LDLCs) have been shown to approach the AWGN channel capacity and can be decoded by a message passing decoder. The messages passed between check nodes and variable nodes are probability density functions, which are approximated by Gaussian mixtures in existing LDLC decoders. However, in the best-known M-Gaussian decoder, the Gaussian mixtures for approximating variable node messages still contain unnecessary Gaussian components, resulting in exponential decoding complexity in the LDLC degree d. In this paper, an efficient LDLC decoder is proposed from the lattice viewpoint, which only finds out important Gaussian components for approximating the variable node messages. The decoding complexity for the proposed decoder is linear in d. Numerical results show that the proposed decoder can achieve significant complexity saving without degrading the performance compared with the M-Gaussian decoder. In particular, the runtime saving is 75.3% when the code length is 10000 and d is 7.
Low-density lattice codes (LDLCs) achieve near-capacity performance on additive white Gaussian noise (AWGN) channels. TheMMM-Gaussian decoder is the state-of-the-art message passing decoder for LDLCs in terms of the error performance. However, this decoder has complexityO(Md−1)O(M^{d-1})O(Md−1)with messages represented by Gaussian mixtures, wheredddis the degree of an LDLC andMMMis 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 complexityO(d)O(d)O(d)is proposed. Our simulation results validate that the LPE decoder achieves almost the same error performance as theMMM-Gaussian decoder.
Low density lattice codes (LDLC) are a family of lattice codes that can be decoded efficiently using a message-passing algorithm. In the original LDLC decoder, the message exchanged between variable nodes and check nodes are continuous functions, which must be approximated in practice. A promising method is Gaussian approximation (GA), where the messages are approximated by Gaussian functions. However, current GA-based decoders share two weaknesses: firstly, the convergence of these approximate decoders is unproven; secondly, the best known decoder requires O(2d)O(2^d)O(2d) operations at each variable node, where ddd is the degree of LDLC. It means that existing decoders are very slow for long codes with large ddd. The contribution of this paper is twofold: firstly, we prove that all GA-based LDLC decoders converge sublinearly (or faster) in the high signal-to-noise ratio (SNR) region; secondly, we propose a novel GA-based LDLC decoder which requires only O(d)O(d)O(d) operations at each variable node. Simulation results confirm that the error correcting performance of proposed decoder is the same as the best known decoder, but with a much lower decoding complexity.
Low density lattice codes (LDLC) can be decoded efficiently using iterative decoding, and approach the capacity of the AWGN channel. In the iterative LDLC decoder the messages are Gaussian mixtures. In any implementation, the Gaussian mixtures must be approximated. This work describes a three/two Gaussian parametric LDLC decoder. Internally at the variable node the periodic Gaussian mixtures are approximated with three or two Gaussians, while the messages between nodes are single Gaussians. The proposed approximation is more accurate than the previously-proposed approximation. Numerical results shows that for moderate dimension, e.g. n = 1, 000, the two Gaussian approximation is sufficient for accurate performance. But for large dimension, e.g. n = 10, 000, three Gaussians are needed.
presented a new family of codes called low density lattice codes (LDLC) that can be decoded efficiently and approach the capacity of the AWGN channel. A linear time iterative decoding scheme which is based on a message-passing formulation on a factor graph is given. In the current work we report our theoretical findings regarding the relation between the LDLC decoder and belief propagation. We show that the LDLC decoder is an instance of non-parametric belief propagation and further connect it to the Gaussian belief propagation algorithm. Our new results enable borrowing knowledge from the non-parametric and Gaussian belief propagation domains into the LDLC domain. Specifically, we give more general convergence conditions for convergence of the LDLC decoder (under the same assumptions of the original LDLC convergence analysis). We discuss how to extend the LDLC decoder from Latin square to full rank, non-square matrices. We propose an efficient construction of sparse generator matrix and its matching decoder. We report preliminary experimental results which show our decoder has comparable symbol to error rate compared to the original LDLC decoder. I.
The recent work of Sommer, Feder and Shalvi presented a new family of codes called low density lattice codes (LDLC) that can be decoded efficiently and approach the capacity of the AWGN channel. A linear time iterative decoding scheme which is based on a message-passing formulation on a factor graph is given. In the current work we report our theoretical findings regarding the relation between the LDLC decoder and belief propagation. We show that the LDLC decoder is an instance of non-parametric belief propagation and further connect it to the Gaussian belief propagation algorithm. Our new results enable borrowing knowledge from the non-parametric and Gaussian belief propagation domains into the LDLC domain. Specifically, we give more general convergence conditions for convergence of the LDLC decoder (under the same assumptions of the original LDLC convergence analysis). We discuss how to extend the LDLC decoder from Latin square to full rank, non-square matrices. We propose an efficient construction of sparse generator matrix and its matching decoder. We report preliminary experimental results which show our decoder has comparable symbol to error rate compared to the original LDLC decoder.
Abstract This paper describes a field-programmable gate array (FPGA) implementation of a fixed-point low-density lattice code (LDLC) decoder where the Gaussian mixture messages that are exchanged during the iterative decoding process are approximated to a single Gaussian. A detailed quantization study is first performed to find the minimum number of bits required for the fixed-point decoder to attain a frame error rate (FER) performance similar to floating-point. Then efficient numerical methods are devised to approximate the required non-linear functions. Finally, the paper presents a comparison of the performance of the different decoder architectures as well as a detailed analysis of the resource requirements and throughput trade-offs of the primary design blocks for the different architectures. A novel pipelined LDLC decoder architecture is proposed where resource re-utilization along with pipelining allows for a parallelism equivalent to 50 variable nodes on the target FPGA device. The pipelined architecture attains a throughput of 10.5 Msymbols/sec at a distance of 5 dB from capacity which is a 1.8 ×\times× × improvement in throughput compared to an implementation with 20 parallel variable nodes without pipelining. This implementation also achieves 24 ×\times× × improvement in throughput over a baseline serial decoder.