Non-binary Hybrid LDPC Codes: Structure, Decoding and Optimization

Abstract: 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.