  Linear nested codes, where two or more sub-codes 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 low-density
parity-check (SC-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. Since the
parity-check matrices of different nested sub-codes partially overlap, the
optimization of one nested sub-code imposes constraints on the optimization of
the other sub-codes. To tackle these constraints, a multi-step optimization
process is applied first to one of the nested codes, then sequential
optimization of the remaining nested codes is carried out based on the
constraints imposed by the previously optimized sub-codes. Results show that
the order of optimization has a significant impact on the number of dominant
absorbing sets in the Tanner graph of the code, resulting in a tradeoff between
the performance of a nested code structure and its optimization sequence: the
code which is optimized without constraints has fewer harmful structures than
the code which is optimized with constraints. We also show that for certain
code parameters, dominant absorbing sets in the Tanner graphs of all nested
codes are completely removed using our proposed optimization strategy.
