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IEEE OPEN JOURNAL OF THE COMMUNICATIONS SOCIETY 2024年 5卷 4322-4336页

作者： Wiriya, Warangrat Kurkoski, Brian M. Japan Adv Inst Sci & Technol Sch Informat Sci Grad Sch Adv Sci & Technol Nomi 9231292 Japan

This paper proposes reliability-based decoding for complex low-density lattice codes (CLDLC) which can be applied to both Gaussian and Eisenstein integers. Two major contributions are: first, a decoding algorithm for CLDLC using a likelihood-based reliability function is used to determine the number of complex Gaussian functions at the variable node. This allows each message to be approximated by a variable number of Gaussian functions depending upon its reliability. An upper bound on the Kullback-Leibler (KL) divergence of the approximation is formed to find selection thresholds via linear regression. Second, a construction of CLDLC using Eisenstein integers is given. Compared to Gaussian integers, this reduces the complexity of CLDLC decoding by exploiting the structure of the Eisenstein integers. The proposed CLDLC decoding algorithm has higher performance and lower complexity compared to existing algorithms. When the reliability-based algorithm is applied to Eisenstein integer CLDLC decoding, the complexity is reduced to O(n.t. 1.35(d-1)) at the volume-to-noise ratio of 6 dB, for lattice dimension n, with degree d inverse generator matrix and t decoding iterations. Decoding CLDLC using Eisenstein integers has lower complexity than CLDLC using Gaussian integers when n >= 49 .

关键词： Lattices Decoding Codes Reliability Complexity theory Iterative decoding Approximation algorithms Complex low-density lattice codes low-density lattice codes parametric decoder lattice decoder Eisenstein integers Gaussian integers

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The Three/Two Gaussian parametric LDLC Lattice Decoding Algorithm and Its Analysis

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IEEE TRANSACTIONS ON COMMUNICATIONS 2016年第9期64卷 3624-3633页

作者： Hernandez, Ricardo Antonio Parrao Kurkoski, Brian M. Japan Adv Inst Sci & Technol Sch Informat Sci Nomi 9231292 Japan

Low density lattice codes (LDLCs) are high-dimensional lattices with a sparse inverse generator matrix that can be decoded efficiently using iterative decoding. In the iterative LDLC decoder, the messages are Gaussian mixtures, and for any implementation, the Gaussian mixtures must be approximated. This paper describes a parametric LDLC decoding algorithm, where internally at the variable node, infinite Gaussian mixtures are approximated with three or two Gaussians, while the messages between nodes are single Gaussians. Strengths of the algorithm include its simplicity and suitability for analysis. Analysis is performed by evaluating the Kullback-Leibler divergence between the true messages and the three/two Gaussian approximation. The approximation using three or two Gaussians is more accurate than previously proposed approximations. Also, noise thresholds for the proposed LDLC decoder are presented, and the proposed decoder reduces the noise thresholds 0.05 dB compared with previous parametric decoders. The numerical results show that for n = 100 and n = 1000, the two-Gaussian approximation is the same as the full-complexity decoder. But when the dimension is n = 10 000, a three-Gaussian approximation is needed.

关键词： Low-density lattice codes parametric decoder lattice decoder

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