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首页> 外文期刊>IEEE Transactions on Information Theory >Multilevel LDPC Lattices With Efficient Encoding and Decoding and a Generalization of Construction $ext{D}'$
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Multilevel LDPC Lattices With Efficient Encoding and Decoding and a Generalization of Construction $ext{D}'$

机译：高效编码和解码以及构造通用化的多级LDPC格 $ text {D}'$

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摘要

Lattice codes are elegant and powerful structures that not only achieve the capacity of the additive white Gaussian noise (AWGN) channel but are also a key ingredient to many multiterminal schemes that exploit linearity properties. However, constructing lattice codes that can realize these benefits with low complexity is still a challenging problem. In this paper, efficient encoding and decoding algorithms are proposed for multilevel binary low-density parity-check (LDPC) lattices constructed via Construction D' whose complexity is linear in the total number of coded bits. Moreover, a generalization of Construction D' is proposed, which relaxes some of the nesting constraints on the parity-check matrices of the component codes, leading to a simpler and improved design. Based on this construction, low-complexity multilevel LDPC lattices are designed whose performance under multistage decoding is comparable to that of polar lattices and close to that of low-density lattice codes on the power-unconstrained AWGN channel.
机译：格码是优雅而强大的结构，不仅可以实现加性高斯白噪声（AWGN）通道的容量，而且还是许多利用线性特性的多端子方案的关键要素。然而，构造能够以低复杂度实现这些益处的晶格码仍然是一个具有挑战性的问题。本文提出了一种有效的编码和解码算法，用于通过构造D'构建的多级二进制低密度奇偶校验（LDPC）格，其复杂度在总编码位数中呈线性。此外，提出了结构D'的一般化，它放宽了对组件代码的奇偶校验矩阵的嵌套约束，从而导致了设计的简化和改进。基于此构造，设计了低复杂度的多级LDPC晶格，其在多级解码下的性能可与无极功率AWGN信道上的极性晶格相比，并且接近于低密度晶格码。

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