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.

中文翻译：

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全局耦合有限几何和有限域 LDPC 编码方案

本文提出了两种类型的级联 LDPC 编码方案，它们被视为 广义全局耦合（ GC ） LDPC 编码方案，其中外码作为 用于纠正局部错误的局部代码和内部代码用作 全局耦合代码来纠正全局错误。第一种级联LDPC编码方案全局耦合有限几何（FG）LDPC码作为局部码和有限域（FF）LDPC码作为全局耦合码。这种类型的全局耦合，称为GC-FG/FF-LDPC 耦合，结合了 FG 和 FF-LDPC 码的独特特征，以在快速解码收敛和接近香农极限的错误性能下实现低错误率。GC-FG/FF-LDPC 码的解码在两个迭代阶段，全局/本地或本地/全局。在第二种级联LDPC编码方案中，局部和全局耦合码都是FF-LDPC码。如果局部耦合码和全局耦合码都由同一个有限域构造并具有相同的图形结构，则GC-FF/FF-LDPC码可以一阶段或两阶段迭代译码，否则，可以分两阶段译码. GC-FF/FF-LDPC 码的构建在长度和速率上非常灵活。所提出的两阶段迭代解码实际上是可以实现的。