  This paper investigates the design and performance of delayed bit-interleaved
coded modulation (DBICM) with low-density parity-check (LDPC) codes. For Gray
labeled square $M$-ary quadrature amplitude modulation (QAM) constellations, we
investigate the optimal delay scheme with the largest spectrum efficiency of
DBICM for a fixed maximum number of delayed time slots and a given
signal-to-noise ratio. When analyzing the capacity of DBICM, we find two
important properties: the capacity improvement due to delayed coded bits being
mapped to the real and imaginary parts of the transmitted symbols are
independent of each other; a pair of delay schemes with delayed coded bits
having identical bit-channel capacity lead to equivalent DBICM capacity. Using
these two properties, we efficiently optimize the delay scheme for any uniform
Gray-QAM systems. Furthermore, these two properties enable efficient LDPC code
designs regarding unequal error protection via bit-channel type
classifications. Moreover, we use protograph-based extrinsic information
transfer charts to jointly optimize degree distributions and channel
assignments of LDPC codes and propose a constrained progressive edge growth
like algorithm to jointly construct LDPC codes and bit-interleavers for DBICM,
taking distinctive bit-channel's capacity into account. Simulation results
demonstrate that the designed LDPC coded DBICM systems significantly outperform
LDPC coded BICM systems.
