Layered schemes for large-alphabet secret key distribution

We discuss the design of practical codes for large-alphabet secret key distribution, motivated by the application of high-dimensional quantum key distribution. We introduce and study a simple scheme called layered scheme, which can be treated as a variant of coded modulation. The idea of layered schemes is to first split the observed large-alphabet symbols into bit layers, and to then encode all the bit layers either independently or jointly using binary codes. The channels that we are interested in are more general than the AWGN channels or Rayleigh fading channels studied in coded modulation. We present and compare different implementations of layered schemes, i.e., based on independent parallel encoding or joint encoding, and we investigate different approaches in how to map large-alphabet symbols into bit layers. Both theoretical analyses and simulation results show that layered schemes have good performances on q-ary channels such as uniform-error channels and limited-magnitude-error channels.