Globally Coupled Finite Geometry and Finite Field LDPC Coding Schemes
Globally Coupled Finite Geometry and Finite Field LDPC Coding Schemes
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DOI：
10.1109/tvt.2021.3102178
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发表时间：
2021-09
影响因子：
6.8
通讯作者：
Mona Nasseri;Xin Xiao;B. Vasic;Shu Lin
中科院分区：
文献类型：
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作者：
Mona Nasseri;Xin Xiao;B. Vasic;Shu Lin
本文介绍了两种类型的串联的LDPC编码方案，这些编码方案被视为全球耦合（GC）LDPC编码方案，其中外代码是校正本地错误和内部代码的本地代码，用作校正全局耦合代码以纠正全局错误。串联的LDPC编码方案的第一种类型的全球串联耦合符合有限几何（FG）LDPC代码作为本地代码和有限字段（FF）LDPC代码作为全局耦合代码。这种类型的全局耦合（称为GC-FG/FF-LDPC耦合）结合了FG-和FF-LDPC代码的独特特征，以在快速解码的收敛和接近Shannon限制的错误性能下达到低错误率。 GC-FG/FF-LDPC代码的解码分为两个迭代阶段，分别是全球/本地或本地/全球。在第二种类型的串联LDPC编码方案中，本地和全局耦合代码都是FF-LDPC代码。如果局部和全局耦合代码都是从相同的有限字段构建的，并且具有相同的图形结构，则可以在一个或两个阶段中迭代地将GC-FF/FF-LDPC代码解码，否则可以在两个阶段中解码。 GC-FF/FF-LDPC代码的构建长度和速率非常灵活。所提出的两相迭代解码实际上是可以实现的。
This paper presents two types of concatenated LDPC coding schemes which are viewed as generalized globally coupled (GC) LDPC coding schemes in which outer codes serve as the local codes for correcting local errors and inner codes serve as global coupling codes to correct global errors. The first type of concatenated LDPC coding scheme globally couples a finite geometry (FG) LDPC code as the local code and a finite field (FF) LDPC code as the global coupling code. This type of global coupling, called GC-FG/FF-LDPC coupling, combines the distinct features of both FG- and FF-LDPC codes to achieve low error rates at a rapid decoding convergence and an error performance close to the Shannon limit. Decoding of a GC-FG/FF-LDPC code is carried out in two iterative phases, global/local or local/global. In the second type of concatenated LDPC coding scheme, both local and global coupling codes are FF-LDPC codes. If both local and global coupling codes are constructed from the same finite field and have the same graphical structures, a GC-FF/FF-LDPC code can be decoded in one phase or two phases iteratively, otherwise, it can be decoded in two phases. Construction of GC-FF/FF-LDPC codes is very flexible in lengths and rates. The proposed two-phase iterative decoding is practically implementable.