Highly flexible design of multi-rate multi-length quasi-cyclic LDPC codes

The design of Low-Density Parity-Check (LDPC) codes with fixed code rate and block length for a fixed channel condition has been well investigated and very close-to-capacity performance can be achieved by careful optimization of a code's degree distributions. The growing variety of services supported by mobile communication systems, however, constitutes the need for highly flexible Forward Error Correction (FEC) schemes. Pursuing this need, we present a design method for the construction of quasi-cyclic (QC) LDPC codes supporting arbitrarily many block lengths and code rates using only a single common mother code. Different block lengths are achieved by an optimized expansion of the mother code's lifting matrix. For the support of multiple code rates, a joint optimization of shortening and puncturing distributions as well as an optimized check matrix construction based on the progressive edge-growth algorithm is employed.