Non-Uniform Spatial Coupling for Windowed Decoding of Spatially Coupled LDPC Codes

In this paper, we consider spatially coupled LDPC codes with finite coupling width. Finite coupling width is important for realizing practical codes that are decoded using, e.g., windowed decoders. We show that by carefully optimizing the amount of coupling in each SP, we can construct codes with excellent thresholds even with the lowest possible coupling factor. We also show that the decoding speed of the wave is faster when using non-uniformly coupled codes. We verify this by carrying out density evolution taking into account windowed decoding and a finite number of iterations. We show that by only slightly increasing the coupling width, excellent codes with close-to-capacity performance can be constructed that lend themselves to practical utilization. Finally, we give some indications on protograph design.