  Graph based codes such as low density parity check (LDPC) codes have been
shown promising for the information reconciliation phase in quantum key
distribution (QKD). However, existing graph coding schemes have not fully
utilized the properties of the QKD channel. In this work, we first investigate
the channel statistics for discrete variable (DV) QKD based on energy-time
entangled photons. We then establish a so-called balanced modulation scheme
that is promising for this channel. Based on the modulation, we propose a joint
local-global graph coding scheme that is expected to achieve good
error-correction performance.
