Globally Coupled Finite Geometry and Finite Field LDPC Coding Schemes

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.