Modified SNR Gap Approximation for Resource Allocation in LDPC-Coded Multicarrier Systems

The signal-to-noise ratio (SNR) gap approximation provides a closed-form 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 trellis-coded 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 low-density parity-check (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 single-user digital subscriber line transmission.