  In this paper, we propose a new design method of irregular spatially-coupled
low-density parity-check (SC-LDPC) codes with non-uniform degree distributions
by linear programming (LP). In general, irregular SC-LDPC codes with
non-uniform degree distributions is difficult to design with low complexity
because their density evolution equations are multi-dimensional. To solve the
problem, the proposed method is based on two main ideas: A local design of the
degree distributions and pre-computation of the input/output message
relationship. These ideas make it possible to design the degree distributions
of irregular SC-LDPC codes by solving low complexity LP problems over the
binary erasure channel. We also find a proper objective function for the
proposed design methodology to improve the performance of SC-LDPC codes. It is
shown that the irregular SC-LDPC codes obtained by the proposed method are
superior to regular SC-LDPC codes in terms of both asymptotic and finite-length
performances.
