  Continuous-variable quantum key distribution utilizes an ensemble of coherent
states of light to distribute secret encryption keys between two parties. One
of the challenges is thereby the requirement of capacity approaching error
correcting codes in the low signal-to-noise (SNR) regime (SNR < 0 dB).
Multilevel coding (MLC) combined with multistage decoding (MSD) can solve this
challenge in combination with multi-edge-type low-density parity-check
(MET-LDPC) codes which are ideal for low code rates in the low SNR regime due
to degree-one variable nodes. However, the complexity of designing such highly
efficient codes remains an open issue. Here, we introduce the concept of
generalized extrinsic information transfer (G-EXIT) charts for MET-LDPC codes
and demonstrate how this tool can be used to analyze their convergence
behavior. We calculate the capacity for each level in the MLC-MSD scheme and
use G-EXIT charts to exemplary find codes for some given rates which provide a
better decoding threshold compared to previously reported codes. In comparison
to the traditional density evolution method, G-EXIT charts offer a simple and
fast asymptotic analysis tool for MET-LDPC codes.
