Comparison between Generalized Integrated Interleaved Codes and Generalized Error Location Codes

Generalized Integrated Interleaved (GII) codes and Generalized Error Location (GEL) codes are both multi-level codes., whose redundancy of each layer is shared by other layers. Original GII codes are defined with a specific conversion matrix., which is studied in detail in this paper. We generalize the conversion matrix for GII codes and make it possible to employ a matrix in row echelon form to reduce the computational complexity of matrix multiplications. It is also shown that with inner codes and outer codes over the same Galois Field., a GEL code degenerates into a GII code. Moreover., the decoding performance is analyzed and some GEL and GII codes are constructed to compare from the aspects of overhead and error performance.