Multilevel Coding Schemes Using LDPC Codes with Signal Shaping for Spectral Efficient Data Communication Systems Multilevel coding (MLC) with multistage decoding (MSD) is an effective approach to combine coding and modulation schemes with the capability of achieving a high degree of both power and bandwidth efficiency. However, signal shaping can further improve the performance of this system by adopting the transmitted constellation points to be unequally likely. In this contribution, we apply the capacity approaching lowdensity paritycheck (LDPC) codes with proper code rates as component codes to the MLCMSD system. Moreover, the system is combined with a tree LDPCbased signal shaping to achieve a shaping gain. Considering different higher order modulation schemes up to 256QAM the combined MLCMSD systems with signal shaping are designed and optimized to effectively operate at high spectral efficiencies up to 0.7 dB. Simulation results show that this combination can offer a shaping gain up to 0.7 dB even for 256QAM schemes.

Modified SNR Gap Approximation for Resource Allocation in LDPCCoded Multicarrier Systems The signaltonoise ratio (SNR) gap approximation provides a closedform expression for the SNR required for a coded modulation system to achieve a given target error performance for a given constellation size. This approximation has been widely used for resource allocation in the context of trelliscoded multicarrier systems (e.g., for digital subscriber line communication). In this contribution, we show that the SNR gap approximation does not accurately model the relation between constellation size and required SNR in lowdensity paritycheck (LDPC) coded multicarrier systems. We solve this problem by using a simple modification   the SNR gap approximation instead, which fully retains the analytical convenience of the former approximation. The performance advantage resulting from the proposed modification is illustrated for singleuser digital subscriber line transmission.