  In this paper, we propose to study and optimize a very general class of LDPC
codes whose variable nodes belong to finite sets with different orders. We
named this class of codes Hybrid LDPC codes. Although efficient optimization
techniques exist for binary LDPC codes and more recently for non-binary LDPC
codes, they both exhibit drawbacks due to different reasons. Our goal is to
capitalize on the advantages of both families by building codes with binary (or
small finite set order) and non-binary parts in their factor graph
representation. The class of Hybrid LDPC codes is obviously larger than
existing types of codes, which gives more degrees of freedom to find good codes
where the existing codes show their limits. We give two examples where hybrid
LDPC codes show their interest.
