With the exponential growth of global internet traffic, it becomes important to increase spectral efficiency for optical transmission systems in order to meet the challenge of continuing capacity growth. Polarization-division multiplexing (PDM) and multi-level quadrature-amplitude modulation (QAM) such as 16QAM allow spectral efficiencies beyond 4 bits/s/Hz. However, for long-haul optical transmission systems, performance is penalized by amplified spontaneous emission (ASE) noise and nonlinearity interference. Moreover, the decreased Euclidean distance between the signal constellation points in high-level QAM modulation formats reduces tolerance to phase noise and distortions. Such reduction in tolerance causes extra performance degradation and limits the transmission distance. In order to counteract this penalty, coded modulation can be used. In coded modulation, part of the redundancy that is usually assigned to forward-error correction (FEC) is moved into symbol modulation to increase the minimum Euclidean distance of a received sequence of symbols. Demodulation is done by a multi-symbol soft-decoder using either maximum likelihood or maximum a posteriori algorithm. In recent publications, LDPC-based bit-interleaved coded-modulation (BICM) with iterative soft-demapping and decoding is used to approach the capacity of AWGN channel, hence increase achievable transmission distance. We review different multidimensional single-parity check (SPC)-based BICM schemes suitable for high spectral efficiency transoceanic transmission systems, and their experimental verification.