  Density evolution (DE) is one of the most powerful analytical tools for
low-density parity-check (LDPC) codes on memoryless
binary-input/symmetric-output channels. The case of non-symmetric channels is
tackled either by the LDPC coset code ensemble (a channel symmetrizing
argument) or by the generalized DE for linear codes on non-symmetric channels.
Existing simulations show that the bit error rate performances of these two
different approaches are nearly identical. This paper explains this phenomenon
by proving that as the minimum check node degree $d_c$ becomes sufficiently
large, the performance discrepancy of the linear and the coset LDPC codes is
theoretically indistinguishable. This typicality of linear codes among the LDPC
coset code ensemble provides insight into the concentration theorem of LDPC
coset codes.
