  In this paper, we propose a type of $G_N$-coset codes for a highly parallel
stage-permuted turbo-like decoder. The decoder exploits the equivalence between
two stage-permuted factor graphs of $G_N$-coset codes. Specifically, the inner
codes of a $G_N$-coset code consist of independent component codes, thus are
decoded in parallel. The extrinsic information of the code bits is obtained and
iteratively exchanged between the two graphs until convergence. Accordingly, we
explore a heuristic and flexible code construction method (information set
selection) for various information lengths and coding rates. Simulations show
that the proposed $G_N$-coset codes could achieve a coding performance
comparable with polar codes but enjoy higher decoding parallelism.
