optimization of Nested Array-based LDPC Codes Via Spatial Coupling

Linear nested codes, where two or more subcodes are nested in a global code, have been proposed as candidates for reliable multi-terminal communication. In this paper, we consider nested array-based spatially coupled LDPC codes and propose a line-counting based optimization scheme for minimizing the number of dominant absorbing sets in order to improve its performance in the high signal-to-noise ratio regime. The presented multi-step optimization process is applied first to one of the nested codes, then an optimization of the remaining nested codes is carried out based on these code constraints. We also show that for certain code parameters, dominant absorbing sets in the Tanner graphs of all nested codes can be completely removed using our proposed optimization strategy.