  In this paper, we first present the asymptotic performance of serially
concatenated low-density generator-matrix (SCLDGM) codes for binary input
additive white Gaussian noise channels using discretized density evolution
(DDE). We then provide a necessary condition for the successful decoding of
these codes. The error-floor analysis along with the lower bound formulas for
both LDGM and SCLDGM codes are also provided and verified. We further show that
by concatenating inner LDGM codes with a high-rate outer LDPC code instead of
concatenating two LDGM codes as in SCLDGM codes, good codes without error
floors can be constructed. Finally, with an efficient DDE-based optimization
approach that utilizes the necessary condition for the successful decoding, we
construct optimized SCLDGM codes that approach the Shannon limit. The improved
performance of our optimized SCLDGM codes is demonstrated through both
asymptotic and simulation results.
